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[Doctoral thesis] High-efficiency heat transfer devices by innovative
manufacturing techniques
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Ventola, Luigi (2016). High-efficiency heat transfer devices by innovative manufacturing techniques.
PhD thesis
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DOI:10.6092/polito/porto/2644177
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Dissertation Politecnico di Torino number : xxxxx
High-efficiency heat transfer devices by innovative manufacturing
techniques
A dissertation submitted to
Politecnico di Torino
for the degree of
Doctor of Philosophy (Ph. D. Polytechnic of Turin)
presented by
Luigi Ventola
M.Sc. Politecnico di Torino
born 9th April 1987
citizen of Italy
accepted on the recommendation of
Prof. Dr. Pietro Asinari, tutor
Dr. Eliodoro Chiavazzo, co-tutor
Torino, 2016
To my parents Armando and Antonietta, and my
beloved Giovanna
Acknowledgements
I would like to thanks Prof. Pietro Asinari and Dr. Elio Chiavazzo, who
supervised my work during last four years. They have guided me during
this long time and have been responsible of my scientific and professional
growth. I learned so much from them and I show gratitude for that. I am
also grateful to Prof. Daniele Marchisio for promoting this collaboration
between me and them.
I would thank people that contributed in achieving scientific results reported in this thesis, namely Flaviana Calignano and Diego Manfredi from
Italian Institute of Technology, Saverio Fotia and Vincenzo Pugliese from
Denso Thermal System S.p.A., and Davide Rondilone from ErreMeccanica
S.r.l.
I would like to acknowledge the THERMALSKIN project: Revolutionary surface coatings by carbon nanotubes for high heat transfer efficiency
(FIRB 2010 - “Futuro in Ricerca”, grant number RBFR10VZUG); It provided me financial support during my first year of work as a research fellow,
paving me the way to the doctorate experience.
Thanks to my parents and grandparents, for their infinite love and support,
for educating me toward honest and simple values. No word can ever be
enough to express gratefulness for them.
Giovanna, thanks for being always by my side. Your love and your incessant encouragement allowed me to overcome my darkest hours.
I owe a special thanks to Pio and Sara, always so close to me. I wish them
will achieve much more important goals than those that I gained.
I would thank my colleagues and friends from Small Lab: Matteo Fasano,
Annalisa Cardellini, Uktam Salomov, Masoud Bigdeli e Matteo Morciano,
for the happy times we spent together, the mutual support, the edifying
suggestions and conversations.
I am happy to mention all students I supervised during their Bachelor and
Master thesis work: Francesco Robotti, Masoud Dialameh, Saverio Affuso,
v
Acknowledgements
Lorenzo Calvara, Davide Canavero, Davide Castignone, Francesca Clerici,
Gabriele Curcuruto, Dario Gigliotti, Rocco Innamorato, Li Yue, Francesco
Locorotondo, Mimmo Geraci, Luqman Herzallah, Francesco Summa, Fabio
Dardano, Nan Zhao, Enrico Treggiari, Tundo Giulia. The mentoring of
these young engineers has been among the most beautiful activities of my
Doctorate, and I thank them all.
Thanks to Marco Vassallo, Antonio Buffo and Gianluca Boccardo, for their
loyal and fraternal friendship.
vi
Ringraziamenti
Ringrazio il Prof. Pietro Asinari e il Dott. Elio Chiavazzo, che hanno
supervisionato il mio lavoro negli ultimi quattro anni. Mi hanno fatto da
guida durante questo lungo periodo di tempo e sono stati responsabili della
mia crescita scientifica e professionale. Ho imparato cosi tanto da loro e
gli sono grato per questo. Grazie inoltre al Prof. Daniele Marchisio, che
ha promosso la collaborazione fra me e loro.
Vorrei ringraziare le persone che hanno contribuito al raggiungimento dei
risultati scientifici riportati in questa tesi, in particolare Flaviana Calignano e Diego Manfredi dell’Istituto Italiano di Tecnologia, Saverio Fotia e
Vincenzo Pugliese di Denso Thermal System S.p.A. e Davide Rondilone
di ErreMeccanica S.r.l.
Un doveroso riconoscimento da parte mia va al progetto THERMALSKIN: Revolutionary surface coatings by carbon nanotubes for high heat
transfer efficiency (FIRB 2010 - “Futuro in Ricerca”, finanziamento RBFR10VZUG), che mi ha fornito il sostegno finanziario durante il mio
primo anno di lavoro come assegnista di ricerca, aprendomi la strada
all’esperienza di dottorato.
Grazie ai miei genitori e i miei nonni, per il loro infinito amore e comprensione, per avermi educato a perseguire sani e semplici valori. Non
basterebberlo le parole per esprimere la gratidudine che provo per loro.
Giovanna, grazie per essere sempre al mio fianco. Il tuo amore e il tuo
incoraggiamento incessanti mi hanno permesso di superare i momenti più
bui.
Un ringraziamento speciale a Pio e Sara, che mi sono sempre stati cosi
vicini. Gli auguro di raggiungere traguardi molto più importanti di quelli
ai quali sono arrivato io.
Grazie ai colleghi ed amici dello Small Lab Matteo Fasano, Annalisa Cardellini, Uktam Salomov, Masoud Bigdeli e Matteo Morciano, per i bei
momenti passati assieme, il reciproco sostegno, i suggerimenti e le conversazioni edificanti.
vii
Ringraziamenti
Sono anche felice di menzionare tutti gli studenti che ho supervisionato durante la loro attività di tesi: Francesco Robotti, Masoud Dialameh,
Saverio Affuso, Lorenzo Calvara, Davide Canavero, Davide Castignone,
Francesca Clerici, Gabriele Curcuruto, Dario Gigliotti, Rocco Innamorato, Li Yue, Francesco Locorotondo, Mimmo Geraci, Luqman Herzallah,
Francesco Summa, Fabio Dardano, Nan Zhao, Enrico Treggiari, Tundo
Giulia. L’attività di tutoraggio di questi giovani ingegneri è stata fra le
più belle del mio dottorato, e di questo li ringrazio.
Grazie a Marco Vassallo, Antonio Buffo e Gianluca Boccardo per la loro
amicizia leale e fraterna.
viii
Contents
Acknowledgements
v
Ringraziamenti
vii
List of Figures
xi
List of Tables
xv
Nomenclature
xvii
1. Introduction
1
2. Optimization of traditional heat exchanger: extruded heat sink 5
2.1. Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.2. Theoretical model for PFHS . . . . . . . . . . . . . . . . . .
7
2.3. Experimental validation of model . . . . . . . . . . . . . . . 13
2.4. Optimization procedure and results . . . . . . . . . . . . . . 17
2.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3. Experimental rig: a purposely developed heat
3.1. Motivations . . . . . . . . . . . . . . . . .
3.2. Limitation of traditional diffusion meters .
3.3. Design of a new sensor . . . . . . . . . . .
3.3.1. The key idea . . . . . . . . . . . .
3.3.2. Mechanical design . . . . . . . . .
3.3.3. Computational support to design .
3.4. Experimental rig description . . . . . . . .
3.4.1. Experimental equipment . . . . . .
3.4.2. Experimental procedure . . . . . .
3.5. Experimental rig validation . . . . . . . .
3.6. Discussion . . . . . . . . . . . . . . . . . .
flux sensor
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ix
Contents
4. Patterns of micro-protrusions for enhanced convective heat transfer
47
4.1. Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2. Design of experiments . . . . . . . . . . . . . . . . . . . . . 48
4.3. Experimental characterization and data reduction . . . . . . 53
4.4. Thermal fluid-dynamics features of micro-protruded patterns 59
4.5. Optimization methodology for micro-protruded patterns . . 61
4.6. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5. Rough surfaces with enhanced heat transfer by direct metal laser
sintering
5.1. Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2. Rough surfaces by direct metal laser sintering (DMLS) . . .
5.3. Morphological and radiative characterization of rough surfaces
5.4. Experimental results . . . . . . . . . . . . . . . . . . . . . .
5.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
69
70
75
79
84
6. Pitot tube based heat exchanger by DMLS
6.1. Motivations . . . . . . . . . . . . . . . .
6.2. Description of Pitot heat exchanger . . .
6.3. Experimental characterization . . . . . .
6.4. Discussion . . . . . . . . . . . . . . . . .
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7. Conclusions and perspectives
93
7.1. Survey and conclusions . . . . . . . . . . . . . . . . . . . . . 93
7.2. Outlook and perspectives . . . . . . . . . . . . . . . . . . . 94
8. Conflicts of Interest
97
9. Curriculum Vitae
99
Bibliography
103
Appendix
115
A. Computational fluid dynamics (CFD) model
117
B. Data regression procedure
119
C. Commercial versus optimized heat sink
121
x
List of Figures
1.1. Thesis contents are summarized in five conceptual pillars.
Study of an industrial heat exchanger motivates the design
of an ad hoc experimental rig. That allows investigation
of various heat transfer enhancement methodologies. Colors aim to distinguish different manufacturing techniques
involved in each activity. . . . . . . . . . . . . . . . . . . . .
2.1. Heat sink geometry (See Ref. [1]). . . . . . . . . . . . . . .
2.2. Scheme of the thermal resistance network of the considered
heat sink (See Ref. [1]). . . . . . . . . . . . . . . . . . . . .
2.3. Scheme of the bypass phenomenon (See Ref. [1]). . . . . . .
2.4. Scheme of heat spreading phenomenon in a PFHS: red and
yellow represent high and low temperature regions, respectively; arrows represent heat propagation paths (See Ref.
[1]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5. Schematic of experimental test rig used for heat sink characterization. Facility belongs to DENSO™ Thermal Systems
laboratories located in Poirino, Turin, Italy (See Ref. [1]). .
2.6. Comparison between experimental results and modeling predictions on the considered commercial heat sink. Experimental error bar values have been estimated relying on similar measurements [2–7] (See Ref. [1]). . . . . . . . . . . . .
3
7
8
9
12
15
17
3.1. Example of a heat flow sensor as used in [8] (see Ref. [4]). . 27
3.2. Maddox&Mudawar experimental correlation [8] re-formulated
in terms of Nusselt number based on the average convective
heat transfer coefficient according to the Eq. (3.8) (solid
line) vs the CFD results (dot-dashed). Error bars with amplitude ± 13.9 % are shown as vertical bars for the Maddox&Mudawar experimental correlation (see Ref. [4]). . . . 31
xi
List of Figures
3.3. Isometric view of the proposed sensor is shown in (a). The
design process has been assisted by a three-dimensional numerical model solving the energy balance equation, depicted
in (b). This model is particularly useful to compute the
sample-to-guard coupling transmittance k. To this purpose,
the guard heater location does not play a crucial role (k
mainly depends on the sensor geometry), and particularly
in the model the heater is placed at the bottom of the guard,
while in the isometric view it is displayed laterally (see Ref.
[4]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
3.4. Schematic diagram of the experimental facility (see Ref. [4]). 35
3.5. Comparison between experimental data, Maddox&Mudawar
experimental correlation[8] and CFD model for aluminum
alloy and copper smooth surface (see Ref. [4]). . . . . . . .
43
3.6. Linear correlation between power given to the sample and
temperature difference between sample and air, for a constant air velocity (see Ref. [4]). . . . . . . . . . . . . . . . .
44
4.1. Sample geometry: Isometric view on left-hand side; Top
view on right-hand side (See Ref. [7]). . . . . . . . . . . . .
49
4.2. Collocation of samples in the model parameter space. Due
to manufacturing tolerances, a non uniform sampling of the
parameter space is considered (See Ref. [7]). . . . . . . . . .
53
4.3. Tested samples (See Ref. [7]). . . . . . . . . . . . . . . . . .
54
4.4. Comparison between experimental (symbols) and model (solid
lines) results in terms of N uL /P r0.33 (See Ref. [7]). . . . . 55
4.5. Comparison between experimental (symbols) and model (solid
lines) results in terms of T r (See Ref. [7]). . . . . . . . . . . 56
4.6. Comparison between experimental (symbols) and model (solid
lines) results in terms of T r/V (See Ref. [7]). . . . . . . . . 57
xii
4.7. Comparison between experimental values of B and the best
fitted analytical model (See Ref. [7]). . . . . . . . . . . . . .
59
4.8. Influence of λp on N uL /P r0.33 (See Ref. [7]). . . . . . . . .
61
4.9. Case study results: Optimal thermal transmittance versus
DPP volume (See Ref. [7]). . . . . . . . . . . . . . . . . . .
64
5.1. (a) Staircase effect on the DMLS model; (b) Building orientation (See Ref. [3]). . . . . . . . . . . . . . . . . . . . . .
71
List of Figures
5.2. Tested samples made of AlSiMg alloy by direct metal laser
sintering (DMLS): (a) sample #1, average roughness Ra =
16 µm; (b) sample #2, Ra = 24 µm; (c) sample #3, Ra = 43
µm; (d) sample #4, finned surface, roughly Ra = 22 µm as
average on both sides (See Ref. [3]). . . . . . . . . . . . . .
5.3. Example of 3D optical scan of sample #5 made by milling
both horizontal surfaces and fin half sides, after testing sample #4. The other physical dimensions remain the same (See
Ref. [3]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4. Process parameters and orientation in the building platform
of the samples produced by DMLS, where P and v are laser
power and scan speed, respectively [9] (See Ref. [3]). . . . .
5.5. Characterization of the residual porosity of the DMLS samples by Field Emission Scanning Electron Microscopy (FESEM): No sub-surface porosity is visible. (a) sample #1;
(b) sample #4, fin root; (c) sample #4, finned surface, fin
middle (See Ref. [3]). . . . . . . . . . . . . . . . . . . . . . .
5.6. Surface morphological characterization of flat samples: (a,
c, e) by 3D optical scanner referring to the fluid-dynamic
plane and (b, d, f) by Field Emission Scanning Electron
Microscope; (a, b) sample #1, Ra = 16 µm; (c, d) sample
#2, Ra = 24 µm; (e, f) sample #3, Ra = 43 µm (See Ref.
[3]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7. Experimental data about convective heat transfer (sample
#1, #2 and #3, see Fig. 5.2). Smooth sample (Ra ≈ 1
µm) with the identical geometry was used as reference (See
Ref. [3]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.8. Experimental data about convective heat transfer of finned
surfaces (sample #4 and #5, see Figs. 5.2 and 5.3). Smooth
sample (Ra ≈ 1 µm) with the identical geometry was used
as reference. Rau and Rad refer to sample #5 mounted with
smooth half fin upstream and downstream, respectively (See
Ref. [3]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1. Heat exchanger with Pitot tubes embedded into the fins.
(a) Picture of the prototype. Drawings of the prototype:
(b) isometric view; (c, f) front views; (d, e) lateral views.
Dashed lines in (c, e) define the cross-sections represented
in (d, f), (See Ref. [10]). . . . . . . . . . . . . . . . . . . . .
6.2. Reference heat exchanger: plate fin heat sink - PFHS (See
Ref. [10]). . . . . . . . . . . . . . . . . . . . . . . . . . . . .
73
74
74
75
76
79
82
87
88
xiii
List of Figures
6.3. Convective thermal transmittance measured at different Reynolds
numbers, for open Pitot (purple squares), closed Pitot (blue
stars), and reference (pink crosses) heat exchangers (See
Ref. [10]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.4. Schematics of the air flow patterns in the Pitot heat exchanger with (a) open and (b) closed configurations (See
Ref. [10]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
xiv
List of Tables
2.1. Geometrical parameters of the commercially available heat
sink experimentally tested (See Ref. [1]). . . . . . . . . . . .
2.2. Experimental results for the commercially available heat
sink (See Ref. [1]). . . . . . . . . . . . . . . . . . . . . . . .
2.3. Comparison between experimental results (Rja,exp ) and model
predictions (Rja,model ) on the considered commercial heat
sink for different values of approach velocity (vd ), with corresponding percent deviations between model and experiments (See Ref. [1]). . . . . . . . . . . . . . . . . . . . . . .
2.4. Lower (LB) and upper (UB) boundary values for geometry
parameters of the PFHS (See Ref. [1]). . . . . . . . . . . . .
2.5. Initial VS optimized release heat sink geometries (See Ref.
[1]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6. Initial VS optimized release heat sink volumes (See Ref. [1]).
13
16
16
20
21
21
3.1. measured quantities uncertainties and measurement devices
sensitivities (see Ref. [4]). . . . . . . . . . . . . . . . . . . . 39
3.2. Experimental data about convective heat transfer for AlSi10Mg
sample (see Ref. [4]). . . . . . . . . . . . . . . . . . . . . . . 41
3.3. Experimental data about convective heat transfer for copper
sample (see Ref. [4]). . . . . . . . . . . . . . . . . . . . . . . 42
4.1. Design values and associated levels for each model parameter (See Ref. [7]). . . . . . . . . . . . . . . . . . . . . . . . .
4.2. Test matrix [11] (See Ref. [7]). . . . . . . . . . . . . . . . .
4.3. Values of model parameters and extra geometrical quantities for the tested samples (See Ref. [7]). . . . . . . . . . . .
4.4. Optimal design parameters for 0.02 < T r < 0.045 [W/K]
and ReL = 0.5 × 104 (See Ref. [7]). . . . . . . . . . . . . .
4.5. Optimal design parameters for 0.02 < T r < 0.1 [W/K] and
ReL = 104 (See Ref. [7]). . . . . . . . . . . . . . . . . . . .
4.6. Optimal design parameters for 0.02 < T r < 0.1 [W/K] and
ReL = 1.5 × 104 (See Ref. [7]). . . . . . . . . . . . . . . . .
52
52
53
64
65
65
xv
List of Tables
4.7. Optimal design parameters for T r = 0.03 W/K at three
different Reynolds numbers (See Ref. [7]). . . . . . . . . . .
5.1. Thermal properties of parts [12]. Heat treatment (last column) by annealing process for 2 h at 573 K for stress relieve
(See Ref. [3]). . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2. Morphological statistical moments of tested samples (see
Fig. 5.2): R-parameters (Rz and average Ra ); S-parameters
(maximum Sp , average Sa , root mean square Sq , kurtosis
Sku and skewness Ssk ). For sample #4, left and right denote the corresponding sides of the fin. Ar is the roughness
surface area and A is the reference planar area (See Ref. [3]).
5.3. Estimated emissivity of tested samples (see Fig. 5.2): Al
refer to milled smooth samples (Ra ≈ 1 µm) used as reference for computing heat transfer enhancement (See Ref.
[3]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4. Experimental data about convective heat transfer for the
flat reference, i.e. Ra ≈ 1 µm (See Ref. [3]). . . . . . . . . .
5.5. Experimental data about convective heat transfer for the
sample #3, i.e. Ra = 43 µm (See Ref. [3]). . . . . . . . . .
5.6. Experimental data about convective heat transfer for the
(single) finned reference (Ra ≈ 1 µm, smooth). For computing the average convective heat transfer coefficient and
the Nusselt number, the total sample surface area was used
(See Ref. [3]). . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7. Experimental data about convective heat transfer for the
sample #4 (Ra = 22 µm, maximum roughness). For computing the average convective heat transfer coefficient and
the Nusselt number, the total sample surface area was used
(See Ref. [3]). . . . . . . . . . . . . . . . . . . . . . . . . . .
xvi
66
72
78
78
80
81
81
82
Nomenclature
Symbols
A
Bi
cp
D
d
f
H
h
hd
I
K
k
L
L∗
l
m
N
Nu
n
P
Pr
p
surface area [mm2 ]
Biot number [−]
specific heat capacity at constant pressure [J/kg/K]
hydraulic diameter [mm]
cylinder diameter [mm]; protrusion base edge [mm]
friction factor [−]
fin/protrusion height [mm]
convective heat transfer coefficient [W/m2 /K]
hatching distance [mm]
electrical current [A]
localized pressure drop coefficient [−]
core-to-guard thermal transmittance [W/K]; slicing direction [−]
fin length, sensor heating edge [mm]
dimensionless fin length [−]
cylinder length [mm]
wave number [mm−1 ]
fin/protrusion number [−]
Nusselt number [−]
direction normal to a sample face [−]
power [W ]
Prandtl number [−]
pressure [P a]; pitch between neighboring protrusions [mm]
xvii
Nomenclature
Q
Qk
Qr
Qc
q
qloss
Ra
Rp
Rz
Rh
Rwire
Rja
Rjc
Rcs
Rsa
Rspr
Re
Re∗p
r
rsangle
S
Sa
Sku
Sp
Sq
Ssk
s
T
Tr
T r0
t
tb
V
V̇
v
y0
Y0
W
xviii
heat flux [W ]
conductive heat flux [W ]
radiative heat flux [W ]
convective heat flux [W ]
generic independent quantity [n.a.]
conductive heat loss [W ]
average roughness [µm]
peak roughness [µm]
five-peak-valley roughness [µm]
heater electric resistance [Ω]
wire electric resistance [Ω]
junction-to-ambient thermal resistance [K/W ]
junction-to-case thermal resistance [K/W ]
case-to-sink thermal resistance [K/W ]
sink-to-ambient thermal resistance [K/W ]
spreading thermal resistance [K/W ]
Reynolds number [−]
modified spacing Reynolds number [−]
equivalent radius [mm]
angle between the rough surface and the building platform [rad]
surface [m2 ]
average surface roughness [µm]
kurtosis surface roughness [µm]
peak surface roughness [µm]
root mean square surface roughness [µm]
skewness surface roughness [µm]
spacing between neighboring fins/protrusions [mm]
temperature [K]
convective thermal transmittance [W/K]
flat sample convective thermal transmittance [W/K]
fin thickness [mm]
baseplate thickness [mm]
volume [cm3 ], electric potential difference [V ]
volumetric flow rate [m3 /s]
velocity [m/s]
viscous length [mm]
average viscous length [mm]
baseplate width [mm]
Greek symbols
α
∆h
∆N uL
η
ηA
ϑ
κ
λ
λa
λCu
λp
µ
ν
ρ
Σ
Σh,B
σB
σh,B
σh,A
σh
σ
τ
χ
Ψ
significance level [−]; air thermal diffusivity [m2 /s]
centerline-to-average convective correction term [W/m2 /K]
centerline-to-average Nusselt number correction term [−]
dimensionless contact radius [−], emissivity [−]
fin efficiency [−]
aerothermal efficiency [−]
DMLS slicing-to-normal direction angle [rad]
Von Kármán’s constant [−]
thermal conductivity [W/m/K]
thermal conductivity of air [W/m/K]
thermal conductivity of copper [W/m/K]
plane solidity [−]
dynamic viscosity [kg/m/s]
kinematic viscosity [m2 /s]
density [kg/m3 ]
standard uncertainties [n.a.]
type B standard uncertainties on h [W/m2 /K]
Stefan-Boltzmann constant [W/m2 /K 4 ]
type B relative standard uncertainties on h [%]
type A relative standard uncertainties on h [%]
overall relative standard uncertainties on h [%]
ratio between open channel area and heat sink frontal area [−]
dimensionless plate thickness [−], shear stress [N/m2 ]
empirical parameter for spreading resistance [−]
dimensionless spreading resistance [−]
xix
Nomenclature
Subscripts and superscripts
a
app
ax
av
B
b
bp
C
c
ch
D
d
E
exp
f
fg
f luid
g
g1
g2
hs
h
i
j
L
m
n
qi
ref
s
u
W
w
+
xx
air
apparent
axial
average
Blasius
baseplate
bypass
contraction
sample centerline; commercial heat sink
channel
hydraulic diameter
approach; downstream
expansion
experiment
fins
G-10 fiberglass epoxy
FC-72 fluorocarbon liquid
guard (sensor)
upstream guard (sensor)
downstream guard (sensor)
heat sink
heater
index of the i-th quantity/sample
junction
sensor heating edge
adiabatic mixing
root surface
i-th independent quantity
reference
heat source, sample
upstream
working
wall
turbulence dimensionless quantities
1. Introduction
Enhancing efficiency of heat transfer processes and devices is fundamental
in a plenty of the technological applications. Some meaningful examples
are thermal management of electronic devices [13], air conditioning and
refrigeration [14], and blades cooling for gas turbine engines [15].
Concerning electronic devices, their progressive size reduction and increase
in computational performances is inevitably leading to a crucial heat dissipation issue in designing novel components [16]. In spite liquid [17, 18]
and two-phase [19, 20] solutions have been investigated, cooling strategies
based on air are expected to remain a rather convenient and popular approach in the next future, due to their low cost and reliability [21]. These
are the so-called heat sinks.
With regard to air conditioning and refrigeration applications, these usually rely on compact heat exchangers [22]. The latter continuously request
for enhancement in heat transfer efficiency, in order to reduce costs, weight
and footprint. These requirements are very important in transportation
sector (e.g. automotive, aerospace), where reduction of weight and footprint of air conditioning and refrigeration components can lead a reduction
in pollutants and green-house gas emissions.
About gas turbine engines, air under forced convection is used for blade
cooling system in nearly all the practical applications. Due to low thermal
conductivity of air, state-of-the-art blade cooling systems rely on peculiar
techniques to enhance convective heat transfer of air under forced regime
[23]. For example, protrusions called pin fins are used to augment heat
transfer on trailing edge by promoting turbulence and mixing.
The importance of high efficiency heat transfer in a variety of technological
fields has incessantly fed the investigation in enhanced heat transfer. In
order to increase heat transfer efficiency of heat exchangers and devices,
a variety of techniques have been investigated in last decades [24]. This
thesis work focuses on heat transfer enhancement techniques under forced
air convection. Concerning forced convection regime, many augmentation
techniques have been already proposed [25], including plane fins [26, 27],
1
1. Introduction
pin fins [28–30], dimpled surfaces [31–33], surfaces with arrays of protrusions [34, 35], metal foams [36], and scale roughened surfaces [37]. The key
idea behind all the aforementioned heat transfer enhancement techniques
is patterning surfaces devoted to heat transfer in order to (i) increase
heat transfer surface area, and (ii) induce fluid dynamic effects aiming to
enhance convective heat transfer coefficient [38]. As a consequence, geometrical design is fundamental to achieve high efficiency in heat transfer
[38], and manufacturing techniques guaranteeing high geometrical flexibility in fabricating parts (devices) made of high thermally conductive bulk
material, e.g. metal, are claimed to have tremendous potential in design of
high efficiency heat transfer devices. Among them, 3D printing technologies (also referred to as additive manufacturing - AM) for metal materials,
seem to be promising in thermal applications [39]. Nowadays, AM is an
economical way to fabricate single items, small batches, and, potentially,
mass-produced items, and it is used in particular by large aerospace companies. For example, GE Aviation™ (a General Electrics™ branch)
produces a huge number of metallic parts for gas turbine engines, including turbine blades by direct metal laser sintering (DMLS). As previously
pointed out, thermal management of turbine blades is a challenging issue.
Consequently, investigation of AM peculiarities (e.g. complex shapes) devoted to heat transfer augmentation is highly desirable.
The present work aims to face the incessant need of high efficiency heat
transfer solutions requested by many technological fields. Thermal fluiddynamics features of both traditional and advanced heat transfer devices
are studied, and novel optimization strategies are developed. Moreover,
AM techniques are used to design high efficiency heat transfer devices,
through ”think additive” attitude, i.e. exploitation of peculiar features of
AM not allowed by traditional techniques. Content of the thesis is synthesized in Fig. 1.1. In particular, in Chapter 2, the efficiency-to-cost
optimization of an industrial heat exchanger, namely a plate fins heat sink
fabricated by extrusion, is faced. Taking into account the dimensions and
shape constrains associated to extrusion process, a geometrical optimization procedure is applied on a heat sink from a real industrial application
in automotive field. This study relies on an experimental campaign carried
on by DENSO™ Thermal System in their laboratories [1]. Then, an in
house experimental test bench has been developed to experimentally investigate advanced heat transfer enhancement methods. This experimental
rig is introduced in Chapter 3. A novel sensor based on ”thermal guard”
for convective heat fluxes measurements has been conceived, designed and
validated [4]. That is used to measure small heat fluxes (air cooled applica-
2
tions) on small size heat transfer surfaces (i.e. micro-structured surfaces,
such as artificial roughness, micro-protruded patterns and pin fins) and
heat exchangers (e.g. heat sinks) as follows: In Chapter 4, patterns of
micro-pin fins (i.e. micro-protrusions) on flush mounted heat sinks are investigated as a heat transfer enhancement technique. The effect of geometrical and fluid-dynamics lengths is highlighted. Moreover a methodology
suited for efficiency-to-cost optimization of these micro-protruded patterns
by ”not subtractive” technologies (e.g. AM) is designed and tested with
regard to a commercial available pin fin heat sink [7].
Figure 1.1: Thesis contents are summarized in five conceptual pillars.
Study of an industrial heat exchanger motivates the design
of an ad hoc experimental rig. That allows investigation of
various heat transfer enhancement methodologies. Colors aim
to distinguish different manufacturing techniques involved in
each activity.
In Chapter 5, DMLS is exploited to fabricate high efficiency heat transfer surfaces, taking advantage of artificial roughness under fully turbulent
regime. DMLS technique is introduced in detail, and rough surfaces morphology, radiative and convective heat transfer features are characterized.
Finally, experimental evidences are reported on the potential of DMLS in
manufacturing flat and finned heat sinks with a remarkably enhanced convective heat transfer coefficient [3]. In Chapter 6 a novel heat exchanger
is designed. Due to its unusual morphology, this device is extremely challenging to be fabricated by traditional manufacturing techniques. Here it
is easily manufactured in one step by DMLS. Remarkable heat transfer
efficiency is achieved. More important, it demonstrates additive manufac-
3
1. Introduction
turing can lead a revolution in conceiving heat transfer devices, when its
extreme flexibility in shapes is fully exploited through ”think additive” approach [10]. Finally, Conclusions and perspectives of this work are drawn
in Chapter 7.
4
2. Optimization of traditional
heat exchanger: extruded heat
sink
In this chapter, a comprehensive thermal model for plate fin heat sinks
(PFHS) is presented and used to optimize heat transfer efficiency of extruded heat sink from a real industrial application in automotive sector.
The model has a broad field of applicability, being comprehensive of the effects of flow bypass, developing boundary layer, fin efficiency and spreading
resistance. Experimental data are used to validate the proposed thermal
model, and demonstrate its accuracy. An optimization methodology based
on genetic algorithms is proposed for efficiency maximization. The latter
maximize the efficiency-to-cost ratio of the heat transfer device, to guarantee a cost-effective selection of the design parameters of PFHS. Such
optimization methodology is then tested on a commercial heat sink, resulting in a possible 64% cost reduction at fixed thermal performances.
Contents of this Chapter can be also found in [1].
2.1. Motivations
In Chapter 1 thermal problems concerning electronic cooling have been discussed and importance of cooling strategies based on air cooled heat sinks
has been argued. In particular, heat sinks with plate fins are among the
most common and studied thermal management solutions for electronic
and automotive devices [40, 41]. Plate fin heat sinks (PFHS) differ in
manufacturing methods (stamping, extrusion, bonding, folding, additive
manufacturing), type of coolant (air, liquid), material (aluminum, copper, alloys, polymeric or composite materials) and flow regime (natural,
forced) [42]. Nowadays, the metal extruded, air-cooled heat sinks are the
most widespread solution, being a satisfactory compromise between costs
and thermal performances [42, 43], both in active (purposely designed
5
2. Optimization of traditional heat exchanger: extruded heat sink
fan) and semi-active (fan already existing in the system) configurations.
However, the choice of the heat sink characteristics maximizing thermal
performances and minimizing production and operating costs for a particular application may be extremely complex, due to the multiple design
options and restraints to be considered at the same time.
In the last decades, many studies focused on a more fundamental understanding of the thermal and fluid-dynamics phenomena involved in aircooled PFHS have been carried out [44–50]. In particular, the main phenomena to be taken into account for a comprehensive thermal model are
(1) base-to-fins spreading resistance, (2) thermal conduction through fins,
(3) boundary layer development along fins, and (4) flow bypass (in case of
unshrouded heat sinks) [42].
Starting from an adequate thermal and fluid-dynamic model, the optimal
configuration for the air-cooled PFHS can be then investigated. To this
purpose, conventional thermal analysis tools are usually inadequate, because both geometry and boundary conditions are not known a priori.
Therefore, numerous optimization procedures have been proposed in the
last years [51–57]. One of the most valid studies on this topic has been
conducted by Culham et al. [58], where a thermal model for shrouded (i.e.
no flow bypass) heat sinks and an optimization procedure based on entropy generation minimization have been coupled. However, optimization
strategies based on entropy generation minimization only focus on operating costs, while neglecting production ones. This may lead to oversizing
the heat sink, which implies an increased amount of material and thus
production costs [59].
Here, both a thermal model and a methodological approach to designing air-cooled PFHS, which allow to optimize the production costs at
given thermal performances, are presented. First, a comprehensive thermal model suited for unshrouded heat sinks is developed, considering the
effect of flow bypass, developing boundary layer along fins, heat conduction through fins and base-to-fins spreading resistance. It is worth to
stress that the proposed thermal model has rather general validity, being
easily applicable also to shrouded heat sink (no flow bypass). Second,
this thermal model is validated by the experimental characterization of
a commercial heat sink for the thermal management of HVAC control
unit in the automotive field. Finally, the thermal model is coupled to
an optimization procedure based on genetic algorithms, in order to find
the optimal geometric parameters of PFHS in semi-active configurations.
That procedure is rather general, taking into account both the full range
6
2.2. Theoretical model for PFHS
of possible working conditions and the technological constrains due to the
adopted manufacturing process (e.g. extrusion, additive manufacturing).
In particular, this optimization methodology is adopted to find the most
cost-effective configuration for the considered commercial heat sink in a
semi-active configuration.
2.2. Theoretical model for PFHS
A comprehensive model for predicting the thermal and fluid-dynamic behavior of air-cooled, unshrouded PFHS under forced convection regime is
here introduced [1].
As schematically depicted in Fig. 2.1, the heat sink geometry considered
in this work is characterized by L, H, t, and N parameters, which are the
fins length, height, thickness and number, respectively. Moreover, W and
tb are the base plate width and thickness, while s is the spacing between
neighboring fins.
Figure 2.1: Heat sink geometry (See Ref. [1]).
7
2. Optimization of traditional heat exchanger: extruded heat sink
The effectiveness of heat dissipation by heat sinks depends on their effective thermal resistance, which is given by the overall effect of thermal
resistances along the heat flux path, from the source to the ambient. Here,
the overall junction-to-ambient thermal resistance (Rja ) of the electronic
package is estimated relying on the classical equivalent thermal resistance
network depicted in Fig. 2.2 [42].
In fact, despite the film resistance at the fluid-solid boundary usually dominates, it has been demonstrated that the effect of other resistance elements
on the heat path cannot be safely neglected in the optimization of the design characteristics of heat sinks [58].
Therefore, Rja is here decomposed in four discrete components, namely:
Rja = Rjc + Rcs + Rsa + Rspr ,
(2.1)
where Rjc , Rcs , Rsa , and Rspr are the junction-to-case, case-to-sink, sinkto-ambient, and spreading resistances, respectively.
Figure 2.2: Scheme of the thermal resistance network of the considered
heat sink (See Ref. [1]).
First, in most applications Rjc is given by the manufacturer, who provides
the electronic components already embedded into the cases. Hence, Rjc
8
2.2. Theoretical model for PFHS
is not directly modeled here, being specific to the considered application
and usually experimentally known.
Second, case-to-sink resistance Rcs is calculated as:
Rcs =
tb
,
λAb
(2.2)
where λ is the thermal conductivity of the heat sink, tb and Ab are the
thickness and cross section surface area of base plate.
Sink-to-ambient resistance Rsa is then computed by analytically modeling
the air flow and pressure drops across the unshrouded heat sink. Note that
the following considerations are safely applicable to any type of flow bypass
(top, side or both) or to fully shrouded configurations. Fig. 2.3 reports the
average air flow velocities in the different sections of the duct where heat
sink is placed, namely: the approach velocity (vd ) at the entrance of the
duct; the channel velocity (vch ) through the channels made by neighboring
fins (fin channels); the bypass velocity (vbp ) in the section of the duct not
occupied by the heat sink.
Figure 2.3: Scheme of the bypass phenomenon (See Ref. [1]).
The air flowing through the fin channels experiences pressure drops due
to contraction and expansion of the flow field at channel inlet and outlet,
respectively. Let us introduce the cross section area of the duct Ad , and
the overall cross section area of the fin channels Ach = (N − 1)sH. The
air flow velocities in the different sections of the duct can be therefore
obtained by applying the conservation of mass and momentum in the duct
[60], namely:
vd Ad = vch Ach + vbp (Ad − Ach )
(2.3)
1
1
2
2
2 ρvbp = 2 ρvch + ∆phs ,
9
2. Optimization of traditional heat exchanger: extruded heat sink
where ρ is the air density and ∆phs is the pressure drop experienced by
air flowing through fin channels. The latter quantity can be decomposed
as:
2
v
L
(2.4)
ρ ch ,
∆phs = KC + KE + 4fapp
Dch
2
where KC and KE are the contraction and expansion pressure drop coefficients, fapp is the apparent friction factor coefficient for developing laminar
flows and Dch = 2s is the hydraulic diameter of the fin channel.
KC and KE take into account the pressure drops generated by the contraction and expansion of flow field at the inlet and outlet of fin channels, respectively. It can be demonstrated that KC = 0.42(1 − σ 2 ) and
KE = (1−σ 2 )σ 2 , where σ = 1−N tW −1 is the ratio between open channels
area and overall frontal area of the heat sink [61]. fapp allows to evaluate
the pressure drop experienced by air while flowing through the fin channel,
and it can be computed as [62]:
11.8
fapp =
L∗
+ (f Rech )2
Rech
12
,
(2.5)
where Rech = ρvch Dch µ−1 is the channel Reynolds number and µ the air
dynamic viscosity; L∗ = L(Dch Rech )−1 is the dimensionless fin length,
whereas the friction factor for fully developed channel flows is:
f=
24 − 32.53
s
H
+ 46.72
s 2
H
− 40.83
Rech
s 3
H
+ 22.96
s 4
H
− 6.09
s 5
H
.
(2.6)
Once the fluid-dynamics quantities within the duct have been fully determined, the sink-to-ambient thermal resistance can be finally computed
as:
1
Rsa =
,
(2.7)
ηhAhs
being Ahs the total heat sink surface involved in the convective heat transfer, h the average convective heat transfer coefficient and η the fin efficiency. The average convective heat transfer coefficient can be calculated
as:
N us λa
h=
,
(2.8)
s
10
2.2. Theoretical model for PFHS
where λa is the thermal conductivity of air and N us can be estimated as
− 31


1

+
N us = 
 (0.5Re∗s P r)3

1

q
3

p
1
1
0.664 Re∗s P r 3 1 + 3.65(Re∗s )− 2
(2.9)
in the range 0.1 < Re∗s < 100 [63]. In Eq. 2.9, Re∗s = 0.5Rech sL−1 is the
modified spacing Reynolds number, P r = µcp,a /λa is the Prandtl number
and cp,a is the specific heat capacity at constant pressure for the flowing
air. The fin efficiency can be then determined as [63]
p
tanh 2N us λa H 2 (t + L)/(λstL)
η= p
.
2N us λa H 2 (t + L)/(λstL)
(2.10)
It is worth to note, in case of unshrouded heat sinks, the main effect of
enhancement in pressure drops induced by the heat sink ∆phs (e.g. due to
reduction of spacing between fins s, hence reduction in Ach ) is to reduce
air velocity over the fins vch and increase bypass velocity vbp (See Eq.
2.3 and Fig. 2.3). As a consequence of diminishing vch , convective heat
transfer coefficient drops down according Eq. 2.9. That can be interpreted
as follows: If heat sink package became too dense (i.e. s reduces) air flow
avoids fin surface and pass through the portion of duct cross section not
occupied by heat sink. As a result, in unshrouded configuration, increase in
∆phs generally could not lead to significant increase pressure drops along
the air circuit, but could lead instead to a significant reduction in heat
sink thermal performances (i.e. convective heat transfer). Hence, relying
on the proposed model, evaluation of thermal parameters implicitly takes
into account pressure drops too.
The fourth thermal resistance considered in the model depicted in Fig. 2.2
takes into account the spreading resistance between the heat source and
the base plate of heat sink. As sketched in Fig. 2.4, spreading resistance
occurs in configurations where heat flows from a small heat source to the
base of a larger heat sink. In this way, the heat cannot uniformly distribute
through the base plate, therefore limiting the convective cooling effect by
the fins.
Spreading resistance is progressively becoming an important issue in modern microelectronics, and it can be mitigated by either increasing the
11
2. Optimization of traditional heat exchanger: extruded heat sink
thickness of the base plate or by adopting materials with higher thermal conductivity (e.g. novel micro- and nano-structured materials [64]).
Here, a perfect thermal contact between case and heat sink base plate (i.e.
negligible thermal contact resistances) is assumed, and Rspr is estimated
following the work by Lee et al. [65], where further details are available.
Let us
p and heat source (i.e. case) equivalent radii as
pdefine the base plate
rb = Ab /π and rs = As /π, respectively, where As is the cross section
area of the heat source.
Figure 2.4: Scheme of heat spreading phenomenon in a PFHS: red and yellow represent high and low temperature regions, respectively;
arrows represent heat propagation paths (See Ref. [1]).
Moreover, let us introduce the dimensionless contact radius () and plate
thickness (τ ):
rs
= ,
(2.11)
rb
tb
τ= .
(2.12)
rb
Considering the dimensionless Biot number of the base plate as Bib =
hrb /λ, it is possible to calculate the dimensionless spreading resistance
Ψ = Ψ(, τ, Bib ) as:
Ψ=
12
χ
tanh(χτ ) + Bi
1
b
(1 − )3/2
,
χ
2
1 + Bib tanh(χτ )
(2.13)
2.3. Experimental validation of model
√
where χ = χ() is an empirical parameter found as χ = π + ( π)−1 [65].
Finally, the spreading resistance Rspr is calculated as:
Ψ
Rspr = √ .
λ As
(2.14)
Even though the overall thermal resistance model for Rja has been developed for unshrouded heat sinks, it is worth to stress that it has general
validity. In fact, it can be easily applied to shrouded heat sinks, by neglecting bypass phenomenon.
2.3. Experimental validation of model
Experiments are carried out to validate the comprehensive thermal model
of the heat sink discussed in Section 2.2. In particular, a commercially
available PFHS (DENSO™ Thermal Systems) is considered as a representative case study. The experimental measurements of the junction-toambient thermal resistance (Rja,exp ) are then compared with the modeling
predictions (Rja,model ), at different approach velocities (vd ) in a semiactive, unshrouded configuration.
Table 2.1: Geometrical parameters of the commercially available heat sink
experimentally tested (See Ref. [1]).
L
[mm]
57.2
W
[mm]
41.4
tb
[mm]
8.4
N
[mm]
14
H
[mm]
21.8
t
[mm]
1
s
[mm]
2.1
The geometrical parameters of the sample heat sink experimentally tested
are reported in Tab. 2.1. The considered heat sink is made out of extruded
AL EN AW 6060 aluminum alloy, and it is currently used for the heat
dissipation of power transistors for the air flow control in HVAC.
The experimental campaign has been designed to thermally characterize
the heat sink in the full range of typical working conditions. Test have
been performed by DENSO™ Thermal Systems in their laboratory for
experimental characterization of HVAC unit located in Poirino, Turin,
Italy. During the tests, the heat sink is flush mounted on one wall of the
HVAC rectangular air duct (cross section area Aduct = 97.67 cm2 ), which
13
2. Optimization of traditional heat exchanger: extruded heat sink
usually feeds the vehicle passenger area. Hence, the heat sink is tested (and
it usually operates) in a semi-active configuration, i.e. it takes advantage
of an existing fan in the HVAC.
The experimental rig used to test HVAC, hence to characterize the heat
sink, is described in the following: air at ambient temperature enters from
the rig inlet pipe of diameter 150 mm, where air flow rate is measured;
Then air flow enters in a plenum chamber of dimensions 2 x 2 x 1.5 m;
Finally, air flow passes through a feeding branch and enters in the HVAC.
HVAC fan is used to flow the air through the experimental rig and into
the HVAC itself.
The transistor voltage drop (V ), electric current (I), junction temperature
(Tj ), and temperature of air approaching heat sink (Ta ) are measured by
a Graphtec™ GL220 data logger. Type T thermocouples are used for
temperature measurements. Consequently, power supplied to the transistor (P = V I) and thermal resistance Rja,exp = (Tj − Ta )/P can be
calculated.
Air flow is measured by orifice plate method. An AISI 304 steel plate is
inserted in the inlet pipe. Orifice in the plate has a diameter of 79 mm.
Pressure taps are inserted upstream and downstream the plate, so that
differential pressure can be measured by a Fuji electric™ FKK differential
pressure transmitter. By measuring differential pressure, volumetric air
flow rate (V̇ ), can be easily calculated [66]. Finally, the approach velocity
can be calculated as vd = V̇ /Aduct .
A schematic of the experimental rig is shown in Fig. 2.5, while experimental results are reported in Tab. 2.2.
Modeling predictions are then obtained relying on Rja,model = Rjc + Rcs +
Rsa +Rspr , as described in Section 2.2. First, Rjc = 0.5 K/W is considered,
as suggested by the manufacturer of the power transistor, which is embedded into the case. Second, Rcs is calculated from Eq. 2.2, considering
Ab = LW = 23.68 cm2 and λ = 209 W/m/K. Third, Rsa is calculated by
means of Eqs. 2.3 - 2.10, considering cp,a = 1013.4 J/kg/K, λa = 0.0259
W/m/K, ρ = 1.1794 kg/m3 , and µ = 1.8415 10−5 kg/m/s. It is worth
mentioning that the lateral area of the base plate is not involved in the
heat transfer phenomenon, because the heat sink is flush mounted on the
wall during the experiments. Consequently, the overall heat transfer area
Ahs can be calculated as:
Ahs = W L + 2(L + t)HN,
14
(2.15)
2.3. Experimental validation of model
Figure 2.5: Schematic of experimental test rig used for heat sink characterization. Facility belongs to DENSO™ Thermal Systems
laboratories located in Poirino, Turin, Italy (See Ref. [1]).
while the overall heat sink volume (V ) as:
V = W Ltb + N tLH.
(2.16)
Finally, Rspr is calculated by Eqs. 2.11 - 2.14, considering As = 1.555
cm2 .
Experimental results and model predictions are compared in Tab. 2.3 and
Fig. 2.6. It can be noticed that model predictions for Rja values are systematically higher than experimental measures. This may be due to the
partial dissipation of P by both radiative (from heat sink to duct walls)
and conductive (through the transistor case holder) heat transfer mechanisms. As a first approximation, radiative and conductive heat transfer
phenomena have been neglected in the thermal model presented in Section 2.2. In fact, the extruded aluminum alloy has low emissivity (≈ 0.1
15
2. Optimization of traditional heat exchanger: extruded heat sink
Table 2.2: Experimental results for the commercially available heat sink
(See Ref. [1]).
V̇
[m3 /s]
0.136
0.125
0.112
0.099
0.086
0.070
0.054
0.036
P
[W]
60.24
76.3
85.07
87.32
82.36
71.4
56.64
38.15
Tj
[◦ C]
84.4
104.3
118
121.9
118.7
111
98.1
86.1
Ta
[◦ C]
26.5
26.1
25.8
25.1
24.8
24.2
23.8
23.1
vd
[m/s]
13.9
12.8
11.5
10.2
8.8
7.2
5.6
3.6
Rja,exp
[K/W]
0.96
1.02
1.08
1.11
1.14
1.22
1.31
1.65
Table 2.3: Comparison between experimental results (Rja,exp ) and model
predictions (Rja,model ) on the considered commercial heat sink
for different values of approach velocity (vd ), with corresponding
percent deviations between model and experiments (See Ref.
[1]).
vd
[m/s]
13.9
12.8
11.5
10.2
8.8
7.2
5.6
3.6
Rja,exp
[K/W]
0.96
1.02
1.08
1.11
1.14
1.22
1.31
1.65
Rja,model
[K/W]
1.18
1.20
1.23
1.26
1.31
1.38
1.49
1.79
Deviation
[%]
22.9
17.3
13.5
13.9
14.7
13.4
13.7
8.4
[43, 67]), whereas the base plate heat sink and transistor case are mounted
in a thermally insulating plastic holder.
Nevertheless, despite convection is the main heat transfer mechanism occurring in flush mounted heat sinks, neglecting radiative and conductive
heat transfer contributions in the experiments leads to slightly underestimate the overall thermal resistance Rja,exp .
16
2.4. Optimization procedure and results
2
Experiment
Model
1.8
Rja [K/W]
1.6
1.4
1.2
1
0.8
5
10
vd [m/s]
15
Figure 2.6: Comparison between experimental results and modeling predictions on the considered commercial heat sink. Experimental
error bar values have been estimated relying on similar measurements [2–7] (See Ref. [1]).
However, the remarkable shape similarity between experimental and modeling results (Fig. 2.6), and their narrow average deviation (15.6%, Tab.
2.3) allow to consider the thermal model presented in Section 2.2 as an
accurate reference for optimizing the plate fins configuration.
2.4. Optimization procedure and results
The majority of existing approaches aims optimizing heat sinks geometry
to achieve the best thermal and fluid-dynamics performances at the same
time [26, 42, 58], in order to fulfill the thermal dissipation requirements
with minimum operating costs (i.e. fan power, which is directly linked to
pressure drops). Differently, the present study focuses on optimizing the
material needed to manufacture a heat sink while meeting the requested
thermal performances, in order to reduce production costs. This approach
17
2. Optimization of traditional heat exchanger: extruded heat sink
is particularly effective in case of unshrouded PFHS operating in semiactive configurations, namely when the air flows on the heat sink thanks
to an already existing fan, and thus no additional operating costs are
generally involved. In particular, being unshrouded, increase of pressure
props induced by heat sink lead to augmentation of bypass phenomenon.
Hence, overall air circuit pressure do not increase, while thermal dissipation
decreases. Here, the optimization procedure is introduced and then tested
on a case study, namely the heat sink tested in Section 2.3.
First, the optimization algorithm takes as inputs the thermal conductivity
of the heat sink material (λ), the maximum values of heat sink thermal resistances (Rja,W ) to be guaranteed for different approach velocities (vd,W ,
i.e. the working conditions), and a first guess geometry. Then, the optimization procedure finds the heat sink geometry that: (1) guarantees
Rja ≤ Rja,W for each vd,W (i.e. the problem constraints); and (2) minimize the heat sink volume, hence the production cost.
This tool considers the heat sink volume, i.e. the amount of material
needed to manufacture the part, as the cost index. Consequently, it is suitable to deal with heat sinks manufactured by ”not subtractive” techniques,
both traditional (e.g. extrusion, casting, stamping, folding [42]) and innovative (e.g additive manufacturing [3, 4, 7], carbon nanotube bundles [2])
ones.
Despite cost optimization generally means both production and operating
costs minimization, here only production costs (i.e. heat sink volume and
thus material amount) are considered for the optimization procedure. In
fact, operating costs come from the power consumption of the dedicated
fan, which is directly linked to the overall pressure drops of the circuit
where the heat sink is placed. However, the optimization procedure suggested in this study is particularly designed for the common case of heat
sinks in unshrouded semi-active configurations, where pressure drops induced by heat sink are usually negligible if compared with other pressure
drops in the circuit, i.e. augmentation in ∆phs do not lead to augmentation in overall circuit pressure drop, but lead to augmentation of bypass
effect. Hence, operating costs can be considered as independent from the
heat sink geometry and, consequently, the cost optimization becomes a
sole production cost minimization [68].
Nevertheless, it is worth stressing that the generality of the reported
procedure is not affected. In fact, the optimization strategy proposed
can be easily adapted for operating costs by substituting V with 1/ηA
18
2.4. Optimization procedure and results
N u/N u
(ηA = (f /fref )ref
0.33 is the aerothermal efficiency [69]) as the cost indicator
to be minimized. In such a way, the proposed optimization methodology finds the heat sink configuration able to minimize the overall pressure
drop due to the heat sink, which determines the additional fan power consumption and thus operating costs. The latter could be relevant in case of
shrouded heat sink, where bypass phenomenon do not take place.
Considering real applications, the set of possible heat sink geometries is
extremely large. Hence, an algorithm able to explore the geometry parameters space in a ”smart” way is needed to find the optimal solution while
spending a reasonable amount of computational time. In this study, genetic algorithms are exploited to guide the problem minimum search with
a more rational generation of the heat sink geometries to be evaluated.
Genetic algorithms are used to minimize an objective function (V ) while
respecting some problem constraints (Rja ≤ Rja,W ). Starting from the
first guess solution given as input, the algorithm randomly generates a
set of possible solutions for the problem (heat sink geometries), which is
called initial population. For each of those possible solutions, the algorithm
checks whether problem constraints are verified or not, and it evaluates the
objective function. Among the solutions within the problem constraints,
the algorithm chooses the ones with the smallest values of the objective
function. Starting from the chosen solutions, the algorithm then generates
a new population (i.e. a new set of possible solutions), relying on crossover
and mutation operators. Therefore, the algorithm is designed to guide
the evolution of the population toward a global, optimal solution. The
population generation process is repeated until a termination condition is
met, such as reaching a plateau in the objective function value or exceeding
a certain number of generations.
The proposed heat sink optimization algorithm is implemented in the
MATLAB™ environment. Basically, the ga function is here adopted to
generate successive iterations of possible heat sink geometries. The thermal model defined in Section 2.2 and experimentally validated in Section
2.3 is then used to compute Rja corresponding to each generated solution
and working condition. Geometries with Rja > Rja,W are then discarded,
whereas the heat sink volume (V ) is computed for the remaining ones. The
latter is the objective function to be minimized by the genetic algorithm.
Lower and upper boundary values for each geometry parameter can be
specified in the genetic algorithm routine.
The heat sink characterized in Section 2.3 is then considered as a test case
for the suggested optimization strategy. The actual geometry and material
19
2. Optimization of traditional heat exchanger: extruded heat sink
parameters of the heat sink by DENSO™ Thermal Systems are adopted
as first guess geometry for the genetic algorithm (see Tab. 2.1). Regarding
the problem constrains, it is imposed that the thermal resistances of the
optimized solution (Rja ) must be equal or lower than the ones predicted
for the commercial heat sink (i.e. Rja,W = Rja,model , as from Tab. 2.3),
for each working condition considered (i.e. vd,W = vd , as from Tab. 2.3).
The boundary values for the geometry parameter imposed in the optimization problem are reported in Tab. 2.4, being dictated by the peculiar
manufacturing technique (extrusion in this case) [42].
Although genetic algorithm optimization schemes are already embedded
in MATLAB™ environment by ga function, choosing proper settings for
genetic algorithm is fundamental to achieve an optimal solution [70]. In
particular, the ga settings adopted are: 100 generations (maximum iteration number); 100 population size (number of solutions generated by ga at
each iteration); 95% crossover rate (ratio between crossover and mutation
operators usage in generating a new population) and 10−14 TolFun (lower
bound for the change of objective function below which optimal solution
is considered to be reached).
Table 2.4: Lower (LB) and upper (UB) boundary values for geometry
parameters of the PFHS (See Ref. [1]).
LB
UB
L
[mm]
10
100
W
[mm]
10
100
tb
[mm]
1
10
H
[mm]
10
80
N
2
20
t
[mm]
0.8
2
Tab. 2.5 reports a comparison between the initial geometry of the commercial heat sink and the one obtained by the optimization procedure.
Moreover, the base plate (Vb ), fins (Vf ) and overall (V ) volumes of initial
and optimized heat sinks are reported in Tab. 2.6. Results show that
the optimal heat sink volume is 13.4 cm3 , that is a remarkable 64% less
respect to the actual commercial heat sink volume (37.4 cm3 ). Therefore,
the presented optimization procedure would allow to save 24 cm3 of material and thus reduce production costs, without affecting the overall thermal
performances of the heat sink (i.e. Rja ≤ Rja,W for each vd,W ).
20
2.5. Discussion
Table 2.5: Initial VS optimized release heat sink geometries (See Ref. [1]).
Initial
Optimized
L
[mm]
57.2
19.4
W
[mm]
41.4
40.7
tb
[mm]
8.4
4.1
N
[mm]
14
20
H
[mm]
21.8
32.9
t
[mm]
1
0.8
b
[mm]
2.1
1.3
Table 2.6: Initial VS optimized release heat sink volumes (See Ref. [1]).
Initial
Optimized
Vb
[cm3 ]
19.9
3.2
Vf
[cm3 ]
17.5
10.2
V
[cm3 ]
37.4
13.4
2.5. Discussion
Given the large amount of geometric, thermal and fluid-dynamics parameters strongly coupled each other, the cost-effective selection and design of
heat sinks for thermal management can be often a complex procedure. In
this Chapter, a comprehensive thermal model of unshrouded plate fin heat
sinks including (1) flow bypass, (2) developing boundary layer along fins,
(3) conduction through fins (fin efficiency), and (4) plate to fins spreading
resistance, has been developed and experimentally validated. The experimental campaign has been carried out to characterize a commercially
available plate fins heat sink, which is currently adopted for automotive
applications (millions of units manufactured per year). Deviations between
experimental results and modeling predictions allow to consider the developed thermal model as an accurate reference for optimizing the plate fins
configuration.
Then, a strategy for the cost optimization of unshrouded PFHS operating
in semi-active configurations has been proposed. Such approach is based
on computationally efficient genetic algorithms and, as a test case, it has
been adopted to optimize the geometry parameters of the commercial heat
sink. The optimized heat sink configuration shows a remarkable 64% volume (i.e. production costs) decrease respect to the commercial one, while
guaranteeing the same thermal performances.
21
2. Optimization of traditional heat exchanger: extruded heat sink
The suggested optimization methodology has been designed for heat sinks
operating in unshrouded semi-active configurations, where the relevant
cost factor is the amount of material used to manufacture the heat sink
(i.e. production cost). However, it is worth to highlight that the reported
procedure is rather general, being easily transferable to operating costs (i.e.
pressure drop) and to a broad variety of thermal management solutions
for electronic and industrial components.
Experimental results shown in this Chapter have been collected by DENSO™
Thermal System in their laboratories. Nevertheless, a more accurate and
flexible test rig is required to investigate different heat transfer enhancement techniques. Consequently, a purposely developed experimental test
bench has been developed in this work. That is described in the following
Chapter.
22
3. Experimental rig: a purposely
developed heat flux sensor
In this Chapter the experimental rig used to characterize the enhanced
convective heat transfer performances of surfaces and devices, proposed
below in this work, is described. That allows to study a plenty of heat
transfer solutions, including (but not limited to) the one investigated in
Chapter. 2. Problems in neglecting conductive and radiative contributions
in a convection dominated heat transfer phenomenon have been pointed
out in the previous Chapter. In particular, them resulted in an underestimation of the convective heat transfer resistance experimentally measured
in Chapter 2. Those difficulties have been solved in this Chapter by designing a novel convective heat flux sensor. That is conceived to exploit
the notion of thermal guard. Sensor is purposely designed to measure
small convective heat flows (<0.2 W/cm2 ) from micro-structured surfaces
and small heat exchangers, that would have been hard to be characterized with enough accuracy by mean of the experimental rig introduced in
Chapter 2. It deals with metal samples, e.g. by DMLS. Sensor design and
validation are described in details. For validation purposes, both experimental literature data and a computational fluid dynamic (CFD) model
are used. Maximum and average deviations from CDF model in terms of
the Nusselt number are on the order of ±13.7% and ±6.3%, respectively
while deviations from literature data are even smaller. Contents of this
Chapter can be also found in [4].
3.1. Motivations
Measuring the convective heat transfer coefficient locally (i.e. on small
ares on the order of 1 cm2 ) usually presents difficulties; The reason (among
others) is that such a quantity depends on both the flow regime and the
fluid properties. Moreover, even though one assumes that the velocity
boundary layer is fully developed (which might not be the case for jets
23
3. Experimental rig: a purposely developed heat flux sensor
impinging on surfaces), still the local convective heat transfer coefficient
strongly depends on the development of the thermal boundary layer. The
latter remark is particularly relevant to electronics cooling, due to small
dimensions of hot spots. In fact, experiments on flush mounted heat sinks
[71–73] clearly show that the local convective heat transfer coefficient is
affected by the chip location on the electronic board. In particular, Authors
in Ref. [71] found that the average convective heat transfer for the rows of
heating arrays decreases approximately 25% from the first to the second
row and by less than 5% from the third to the fourth row. Ref. [72] reports
that, in steady state conditions, heat transfer coefficient is strongly affected
by the number of chips and their locations in the streamwise flow direction.
The latter results have been proved also in transient conditions [73]. The
peak in the convective heat transfer coefficient at the edge of the heating
surface is due to the small thickness of the thermal boundary layer in
the early development region. Small thickness of the thermal boundary
layer makes the developing region ideal to investigate the heat transfer
enhancement due to micro-structures (e.g. process roughness, protruded
patterns). For this reason, in the present Chapter, a single flush-mounted
heat source such as the one considered in [8] is considered.
Classical methods for measuring the local heat flow can be divided in three
main categories: Methods based on thermography, on sensible capacitors
and on diffusion meters [38]. During the past several years, infrared thermography has evolved into powerful tool to measure convective heat fluxes
as well as to investigate the surface flow field over complicated bodies [74].
In spite of the advantages of the latter technique, e.g. the modest intrusiveness [75], infrared thermography suffers from some drawbacks. First of
all, the measurement accuracy depends on the knowledge of the emissivity
coefficient of the surface exposed to the infrared camera [74]. This effect
is more susceptible to highly polished surfaces: In fact, due to low emissivity coefficient and high reflectivity of the surface one has to cope with
a low signal-to-noise ratio [74]. Moreover, surface structuring/patterning
might create problems in estimating non-homogeneous emissivity. In case
of high density applications, there might also be a problem in positioning
the access window to the test surface for the infrared camera [74]. Finally,
when measuring the local convective heat transfer coefficient over a fin,
the temperature value identified at each image pixel by the infrared camera must be post-processed by a numerical model in order to estimate the
desired quantity [76, 77]. Hence, it is an indirect measurement technique,
which might be further affected by the uncertainties of the underlaying
numerical model.
24
3.1. Motivations
Measurements by sensible capacitors require that heat flow is used to transfer energy to a capacitor, where energy is stored in the form of sensible
heat [38]. The heat flux is then measured by the time evolution of the temperature. Large thermal inertia is required, so that the time for thermal
equilibrium is long and easily measurable. It is important that the temperature within the device is as uniform as possible and the volume/surface
area ratio of the capacitor very small. Some disadvantages of sensible
capacitors include inaccuracy in obtaining the time evolution of the temperature, the need to cool down the device to a temperature lower than the
temperature where the heat flow is to be measured before measurements
can be taken and the intrusiveness of the device [38].
On the other hand, diffusion meters are based on the Fourier’s law of
heat conduction at steady state [38]. Here, it is necessary that the heat
flow within the device stays unidirectional. Consequently, some proper
insulation must be ensured and the heat flux can be measured by a series of thermocouples installed along the main heat flow direction. Some
disadvantages of diffusion meters include difficulties in maintaining the
heat flow direction, the need for truly insulating layers around the measuring elements and the need for a steady-state measurement [38]. In
addition, establishing an (easily) measurable temperature gradient in a
highly conductive material requires large thermal fluxes. In case of forced
air convection, thermal fluxes may be quite small (e.g. < 0.2 W/cm2 ) and
this introduces significant difficulties in measuring a temperature gradient
within a copper bar as in Ref. [8], where thermal fluxes larger than 5
W/cm2 are indeed considered. Moreover, in case of small thermal fluxes,
the relative magnitude of the conduction losses increases and it makes less
accurate the measurement by a diffusive meter. It is worth to note that the
conduction losses are, in general, non-linear. In fact, some thermal power
is inevitably lost and reaches the air stream passing through the sensor
holder. More dramatically, the amount of surface area which is crossed
by conduction losses, is affected in turn by convection, thus making the
thermal resistance due to conduction losses flow dependent. In this research activity, the latter issue was experienced during the development
of a previous release of the presented sensor (not reported), and it was
successfully solved by introducing the thermal guard. More details about
the latter issue are provided below in Section 3.2.
Another type of sensor that has recently gained great popularity are flush
mounted sensors [78] [79], which are commonly used in heat transfer characterization of flat surfaces. However for micro-structured surfaces a reliable measure of the convective heat transfer coefficient is difficult to ob-
25
3. Experimental rig: a purposely developed heat flux sensor
tain with those sensors. In fact, if the latter sensors are mounted on
micro-structured surfaces, then the fluid-dynamics interactions between
micro-structures and fluid flow are (at least locally) perturbed. This implies that heat transfer is altered by the presence of the sensor and hence
the measurement is not reliable. On the other hand, positioning such sensors at the bottom of samples is not always an accurate solution, owing
to an unavoidable change of the heat flux direction. Although one might
think that the adoption of insulating materials (surrounding the sample
facets that are not exposed to the fluid) represents an effective solution,
that this may lead to non-negligible deviations in the heat flux estimates as
demonstrated in Section 3.2. In addition, the issue of undesired heat losses
in such convective heat transfer measurements becomes even more serious
when small fluxes are to be measured, thus making questionable the use of
those sensors in the context of micro-electromechanical systems (MEMS),
which is an active research area gaining and increasing popularity (see e.g.
[79, 80]).
Motivated by all this, a sensor that is able to tackle the above drawbacks by
resorting to the notion of thermal guard has been designed and validated
(against both experimental data from literature and a computational fluid
dynamic model). As a result, a few advantages of the proposed device are
summarized in the following:
1. The sensor does not perturb the fluid-dynamic interactions between
micro-structures and fluid flow.
2. The uncertainties due to (spreading) conduction losses can be effectively made negligible by adopting the thermal guard, which keeps
the temperature within the device very uniform.
3. The experimental procedure is remarkably simple, because it only
requires the measurement of an electrical power and three temperatures. No numerical model is required to post-process each time the
measured quantities, leading to a direct measurement technique.
4. The sensor design can be miniaturized, making it an ideal candidate
for studies with small heat fluxes (e.g. forced air convection and
MEMS applications).
5. Unlike state-of-the-art flush mounted foil sensors, which are often
limited in terms of the operating temperature due to delamination
issues (i.e. 120-150 C◦ , see [81]), the present sensor can be easily
designed to withstand high temperatures by a proper choice of materials.
26
3.2. Limitation of traditional diffusion meters
Figure 3.1: Example of a heat flow sensor as used in [8] (see Ref. [4]).
The Chapter is organized as follow. The main traditional approaches for
convective heat transfer measurements are reviewed in Section 3.1. In
Section 3.2, the issue of spreading conduction losses when addressing the
measurement of small heat fluxes by traditional devices is discussed. The
key-idea behind the proposed sensor is presented in Section 3.3.1, whereas
details about the sensor design are provided in Sections 3.3.2 and 3.3.3.
In Section 3.4, the equipment and the procedure adopted in the validation process are discussed. In Section 3.5, the experimental results are
presented and a comparison with both independent experimental data
from literature and the results of a fluid-dynamic model (whose details
are discussed in the Appendix A) are reported. In Section 3.6, results are
discussed.
27
3. Experimental rig: a purposely developed heat flux sensor
3.2. Limitation of traditional diffusion meters
In the following, referring to the diffusion meter utilized in [8], will be highlighted possible issues arising when measuring small heat fluxes, as those
experienced with low thermal conductive fluids (e.g. air) and/or small
heat exchange surface areas (e.g. small chips and/or MEMS devices). The
device proposed in [8] is schematically reported in Fig. 3.1 and, similarly
to the sensor proposed below in this work, utilizes a copper sample (with
slightly different dimensions, namely 12.7 × 12.7 × 5.51 mm3 ) upon which
the convective heat transfer coefficient is to be measured. The latter sample is flush mounted on one side of a flow channel, and surrounded by low
thermal conductive G-10 fiberglass epoxy, for reducing conduction heat
losses. Heat is generated by a cartridge heater positioned at the bottom
of the bar and reaches the sample through a copper bar. The bar is embedded in a G-10 fiberglass flange. While an air gap is present along most
of the bar length (roughly 30 mm), the remaining part of the bar (comparable to the sample thickness) is in direct thermal contact with the G-10
fiberglass epoxy. The temperature gradient (hence the heat flux) through
the copper bar can be measured by means of four thermocouples located
along the centerline of the copper bar. A linear trend of the temperature profile along the bar is demonstrated, hence the local heat flux at
the copper bar axis can be accurately estimated by Fourier’s law. Strictly
speaking, owing to unavoidable conduction heat losses, the above heat flux
is only accurate along the symmetry axis in Fig. 3.1. On the other hand,
if the aim of the study is measuring the heat flux from the entire sample
surface, the average heat flux is the quantity of interest. For instance,
this is certainly true in electronics cooling, where the total dissipated heat
from a chip surface is often the only concern. In those cases, the measurement accuracy of diffusion meters fully relies upon the possibility of
neglecting the conduction heat losses (as compared to the heat flux exiting
the sample surface exposed to the fluid flow) and on the assumption that
the average heat flux can be safely approximated by the value measured
at the centerline. Whenever the above approximation does not hold, the
use of correlations such as the one proposed in [8] (and derived from measurement along the copper bar centerline) clearly leads to overestimates
of the average convective heat transfer. Towards an effort of quantifying
the effect of the conduction heat losses in the experiments reported in [8],
the following analytical formula expressing the conduction heat from a hot
vertical cylinder (copper sample attached to the bar) embedded within a
semi-infinite medium (air gap and G-10 fiberglass epoxy) is invoked (see
28
3.2. Limitation of traditional diffusion meters
Ref. [38] p. 224):
qloss =
2πl
λf g (Ts − Ta ) ,
ln (4l/d)
(3.1)
where l, d and λf g denote the cylinder length, the cylinder diameter and
the thermal conductivity of the fiberglass flange, respectively. The average
convective heat transfer coefficient h over the sample surface can be cast
into the form:
hc L2 (Ts − Ta ) − qloss
h=
,
(3.2)
L2 (Ts − Ta )
where hc is the convective heat transfer coefficient at the centerline (consistently with the one measured in [8]). In the ideal case of qloss = 0, it
follows h = hc . Owing to (3.1), the equation (3.2) reduces to the explicit
expression:
2πl
h = hc − 2
λf g
(3.3)
L ln (4l/d)
By referring to Fig. 3.1, the cylinder presents a square cross-section and
two different media are surrounding its mantel. To first approximation,
even with a conservative assumption of neglecting the heat loss through
the cylinder mantel facing the air gap, it results l ≈ lf g ≈ 11 mm with lf g
being the cylinder length in direct contact with the fiber glass. Finally,
considering G-10 garolite [82] with λf g = 0.27 W m−1 K −1 and an effective cylinder diameter d = 14.3 mm (chosen to preserve the heat transfer
surface area by L2 = πd2 /4), it yields the following estimate:
h ≈ hc − ∆h,
(3.4)
with ∆h = 103 W m−2 K −1 . In [8] an empirical correlation is provided for
samples with a smooth surface:
N ucL = 0.237Re0.608 P r1/3 ,
(3.5)
where the superscript in the Nusselt number N ucL is used to stress that
this quantity is based on measurements of hc : N ucL = hc L/λf luid . In
particular, because an inert flourocarbon liquid (FC-72) is used in the work
of Maddox & Mudawar, the correction term ∆h in equation (3.4) can be
translated in terms of a corresponding Nusselt number as follows:
∆N uL =
103[W m−2 K −1 ] 0.0127[m]
∆hL
≈
= 22.9,
λf luid
0.057[W m−1 K −1 ]
(3.6)
29
3. Experimental rig: a purposely developed heat flux sensor
and consequently the following dimensionless group:
∆N uL
40.1
=
= 9.9,
1/3
Pr
12.31/3
(3.7)
where the Prandtl number is assumed to be P r = 12.3 (see also Fig. 6 in
Ref. [8]). As a result, if the average heat transfer coefficient h is of interest
(instead of hc ), the correlation (3.5) should be expressed as follows:
N uL + ∆N uL
= 0.237Re0.608 ,
P r1/3
(3.8)
where N uL = hL/λf luid and N ucL = N uL + ∆N uL . It is worth stressing
that the above analysis aims at providing only an estimate of the conduction heat losses for the set-up in Fig. 3.1. Hence, for the sake of simplicity,
the contact thermal resistance between the cylinder and the surrounding
medium has been neglected to first approximation. As a consequence, (3.7)
is expected to slightly overestimate the group ∆N uL /P r1/3 .
However,
judging from (3.7), in the low Reynolds numbers regime (e.g. Re ≈ 3000)
and for the analyzed configuration, the influence of the correction term
∆N uL can be on the order of 0.35 N ucL . Hence, as long as the average
convective heat transfer coefficient is of interest, there are certainly conditions where conduction losses cannot be neglected and should be properly
taken into account during the measurement process. The above argument
also shows that, due to difficulties in evaluating the correction term (3.7)
with a desired accuracy (e.g. owing to possible unpredictable thermal contact resistances), the use of diffusion meters (or other sensors suffering
from conduction heat losses) in such a context may become quite problematic.
For the sake of completeness, a computational fluid dynamic (CFD) model
has been developed to compute the average convective heat transfer coefficient through a square shaped sample (consistently with the set-up of
interest for this study). Details of the model are reported in the Appendix
A. Most importantly, it is worth to note that the latter numerical model
is found to be in good accordance with the empirical correlation proposed
by [8], and here re-formulated in terms of the Nusselt number based on
the average convective heat transfer coefficient following Eq.(3.8). The
comparison in reported in Fig. 3.2, where the adoption of a linear vertical
scale (instead of the usual logarithmic one) makes the matching even more
appreciable. Hence, as long as smooth samples are concerned, both an experimental correlation (3.8) and numerical results from CFD are available
for validating the proposed sensor.
30
3.2. Limitation of traditional diffusion meters
90
80
NuL/Pr0.33
70
60
50
40
30
20
10
Maddox&Mudawar (1989)
CFD
0.5
1
ReL
1.5
2
4
x 10
Figure 3.2: Maddox&Mudawar experimental correlation [8] re-formulated
in terms of Nusselt number based on the average convective
heat transfer coefficient according to the Eq. (3.8) (solid line)
vs the CFD results (dot-dashed). Error bars with amplitude ±
13.9 % are shown as vertical bars for the Maddox&Mudawar
experimental correlation (see Ref. [4]).
It is also worth to stress that, although the above discussion focused on
conduction heat losses in a diffusion meter, a similar analysis also applies to
devices where a flush mounted foil sensor is adopted for instance between
the bar and the sample. In fact, reducing at will the heat losses through the
finite thickness of the sample (e.g. by means of insulating materials) is not
a trivial task, especially when the fluid thermal conductivity is comparable
to (or even smaller than) the adopted insulating material.
As a result, in this work, a new sensor for the direct and accurate measurement of the average convective heat transfer coefficient over small surfaces has been designed. In the presented implementation, the sensor is
conceived for dealing with forced air cooling a sample surface (roughly 1
cm2 ), and details are reported in the sections below.
In principle, there are no limitations to a further miniaturization of the sensor. As mentioned in Ref. [79], such a feature is highly desirable and still
31
3. Experimental rig: a purposely developed heat flux sensor
represents a challenge for state-of-the-art flush mounted foil sensors.
3.3. Design of a new sensor
3.3.1. The key idea
The key-idea is to exploit the notion of thermal guard for local convective heat transfer measurements. Guarded hot plate method has been
extensively used in measuring thermal conductivity. When attaching two
thermostats at different temperatures to the opposite faces of the sample,
heat flows from the hot to cold side typically following three-dimensional
paths. However, a one-dimensional flow can be established within a sample by surrounding it with temperature-controlled “guards” designed to
prevent the heat flow in all directions other than the desired one [83].
The ability of the guard to prevent undesired heat flows can be conveniently used for measuring convective heat transfer coefficients as well.
Sensors based on this concept may be so accurate that can be used even
for calibration purposes. For instance, the US National Institute of Standards and Technology (NIST) has developed a convective heat flux facility
to allow calibration of heat flux sensors based on a guarded calibration
plate (30 cm × 10 cm × 3 cm) [84].
In this work, a similar idea is developed at a smaller scale, and used beyond
calibration purposes for developing a simple though accurate sensor. An
isometric view of the proposed sensor is reported in Fig. 3.3. The proposed
sensor is made of three essential parts: (i) sample, (ii) insulation shield
and (iii) guard. A heater is placed at the bottom of the sample and the
latter is made of highly conductive material, because it has to efficiently
transfer heat towards the flushing flow. The sensor presents an onion-like
structure: Insulation shield wraps the sample, while a highly conductive
guard wraps the assembly consisting of both the sample and the insulation
shield. The insulation shield and the guard are shaped such that the guard
sharply joins the sample, and the sensor surface exposed to the air flow
appears as a unique element. As a result, two independent thermal circuits
are obtained, where the sample heater generates the thermal power to be
removed by the tested surface, while an auxiliary heater supplies thermal
32
3.3. Design of a new sensor
energy to the guard until isothermal condition is reached (i.e. negligible
heat transfer between the guard and the sample).
3.3.2. Mechanical design
(a)
(b)
Figure 3.3: Isometric view of the proposed sensor is shown in (a). The
design process has been assisted by a three-dimensional numerical model solving the energy balance equation, depicted in
(b). This model is particularly useful to compute the sampleto-guard coupling transmittance k. To this purpose, the guard
heater location does not play a crucial role (k mainly depends
on the sensor geometry), and particularly in the model the
heater is placed at the bottom of the guard, while in the isometric view it is displayed laterally (see Ref. [4]).
Fig. 3.3 shows the sample (in this realization, a box of 11.1 mm × 11.1 mm ×
5 mm), which is heated at the bottom and cooled from above by air flushing
in a wind tunnel. The top surface of the sample can be possibly patterned
in order to investigate different techniques for heat transfer enhancement.
The sensor sample is heated by an electrical heater (a 12.7 mm × 12.7
mm Minco heater with a nominal resistance of 26.5 Ω). Thermal grease,
with conductivity 2.9 W/m/K, was used for reducing thermal resistances
at all contact surfaces of the device, when appropriate. The sample is surrounded by an insulation shield made of Teflon. This element consists of a
16 mm × 16 mm × 3 mm plate at the bottom and a 2.4 mm-thick squareshaped tapered ring with negligible thickness at the test surface. Finally,
the sample and shield assembly is embedded within the thermal guard
33
3. Experimental rig: a purposely developed heat flux sensor
which comprises a square-shaped complement of the insulation shield on
top of a flat plate. The latter two elements are made of copper and their
mechanical and thermal contact is ensured by two watch screws (M1.6).
The upper part of the guard is built by electrical discharge machining
(EDM) in order to have sharp edges leading to minimal sample/guard
contact (important for having two independent thermal circuits). The
guard heater (same electrical resistance by Minco is used) is positioned
upstream for (partially) compensating the higher convective heat transfer
coefficient due to the development of the thermal boundary layer (induced
by the guard). The sensor assembly is held by an insulator holder made
of nylon, which is fixed to the wind tunnel (discussed below).
Three temperatures are measured by means of Chromel-Alumel (type K)
thermocouples with probe sheath diameter of 0.5 mm. A first thermocouple crosses all layers and reaches the center of the sensor sample. The remaining two thermocouples are inserted in the upstream and downstream
wall, respectively. Although the development of the thermal boundary
layer might lead to small temperature differences streamwise, having three
thermocouples in a row aligned along the fluid flow is twofold advantageous. First, this enables to check that only a minimal temperature differences is established between two sufficiently far locations of the guard
(in this setup, on the order of 0.2 K). Second, imposing that the sample
temperature Ts is the arithmetic mean of the two temperature values in
the guard, namely Ts = (Tg1 + Tg2 )/2, enables to minimize the net heat
exchange between sample and guard due to possible balance mismatches.
3.3.3. Computational support to design
The design process has been assisted by numerical computations. In particular, a three-dimensional numerical model has been developed and solved
by Fluent™. A simplified non-coupled model solves the stationary energy
balance equation within the sensor assembly, assuming a fixed convective
heat transfer coefficient.
Let us suppose to use copper (thermal conductivity 388 W/m/K) for
both the sample and the guard, Teflon™ (0.25 W/m/K) for the insulation shield and nylon (0.25 W/m/K) for the external sensor holder. This
model includes the convective heat transfer as a boundary condition on the
surface in contact with the flushing flow. A fixed convective heat transfer coefficient is assumed for both the sample and the guard, namely 70
34
3.4. Experimental rig description
W/m2 /K. The back side of the sensor is subject to a different boundary
condition due to natural convection with a coefficient of 10 W/m2 /K.
In the model, the thermal power of the sample heater and the one of the
guard heater can be independently controlled. Let us suppose to provide
0.05 W to the sample heater. The balance condition will be defined by
matching the sample temperature Ts , measured at the sample center, and
the guard temperature Tg , measured in the guard lateral wall, up to a
certain precision. Let us suppose that Ts − Tg = 0.2 K and consequently
that part of the power provided by the sample heater flows towards the
guard. The numerical model can be used to evaluate the power lost towards
the guard. In this set-up, it was found to be 0.002 W ), corresponding
to 4 % of the sample heater power. Hence, by linear extrapolation, the
conduction losses towards the guard can be expressed as k (Ts − Tg ) where
k = 0.01 W/K.
It is worth stressing that the transmittance k depends on the sensor geometry, hence it is only required to be computed once for ever (for a given
sensor design).
3.4. Experimental rig description
3.4.1. Experimental equipment
Figure 3.4: Schematic diagram of the experimental facility (see Ref. [4]).
35
3. Experimental rig: a purposely developed heat flux sensor
The flow loop of the experimental system is schematically shown in Fig.
3.4. The developed sensor is installed at the center of the vertical wall of
a horizontal rectangular flow channel, which resembles a small open-loop
wind tunnel. The channel has a smooth inner surface, a cross section of
228 mm×158 mm (hydraulic diameter 187 mm) and an entrance length of
5 m (corresponding roughly to 26 hydraulic diameters). The air is blown
by a Savio s.r.l. centrifugal fan type SFL 25-A (maximum flow rate 70
m3 /min at 420 P a, maximum pressure difference 1900 P a at 18 m3 /min),
with a throttling valve for regulating the mass flow rate. At the end of
the channel, downstream from the test section, a vane anemometer Testo
450 by Testo AG (sensitivity ±0.1 m/s) was used for measuring the axial
velocity. The air temperature is measured at the same location where the
anemometer is installed (not affected by the power released by the convective sensor). The thermocouple probe sheath is embedded in a block
of polystyrene foam, covered by an aluminum foil, ensuring stable measurements and negligible effects due to radiation. Similarly, the channel
wall temperature is measured by a thermocouple installed on the inner
surface of the channel, covered by a block of polystyrene foam with an
external aluminum foil. Also in this case, Chromel-Alumel (type K) thermocouples were used. Two HQ PS3003 variable power suppliers (voltage
range 0 − 30 V and 0 − 3 A) are used to feed both the sample and the
guard heater. Finally, a six-digits, electronic multimeter (Agilent 34401A)
is used to measure the voltage to the sample heater circuit, made of the
heater itself and the wires to connect the heater to the power supplier.
3.4.2. Experimental procedure
The axial velocity vax , measured by the vane anemometer, is used to compute the Reynolds number RexD = vax D/ν where D is the hydraulic diameter of the channel. However, it is worth to note that the experimental
data are usually reported in terms of a differently defined Reynolds number ReD = vav D/ν, which depends on the average velocity vav instead.
These two velocities have been correlated by a purposely-developed fluiddynamic numerical model, which was solved by Fluent™ and described in
the Appendix A. The previous numerical model was used to construct the
1.0162
following relation, ReD = 0.694 (RexD )
, which correlates the average
velocity to the axial velocity (measured by the vane anemometer) through
the corresponding Reynolds numbers.
For computing the average convective heat transfer coefficient at the sam-
36
3.4. Experimental rig description
ple surface, the following relation is used
h=
Vh2 /Rh − σB A(Ts4 − Tw4 ) − k[Ts − (Tg1 + Tg2 )/2]
,
A(Ts − Ta )
(3.9)
where Vh is the potential difference across the sample resistance, Rh is the
sample resistance, σB = 5.67 × 10−8 W/m2 /K 4 is the Stefan-Boltzmann
constant, is the emissivity of the sample surface, Ts is the sample temperature measured by the thermocouple inserted in the center of the sample,
Tw is the temperature of the channel wall, k = 0.01 W/K is the sampleto-guard coupling transmittance (see Section 3.3.3), Tg1 and Tg2 are the
temperatures measured by the (upstream and downstream) thermocouples
installed into the thermal guard, A = 1.23 cm2 is the flat sample surface
and, finally, Ta is the air temperature. Vh is calculated by the following
equation:
Rh
Vh = V
,
(3.10)
Rh + Rwire
where V is the voltage applied to the sample heater circuit, measured by
the multimeter for each test, while Rwire is the resistance of heater wires,
which measures 0.015 Ω. Before proceeding with the experimental results,
a discussion about the estimate of uncertainties and their propagation by
the proposed measurement chain is required. Eqs. (3.9) and (3.10) allow
to compute h as a function of other measurements (V, Ts , Tg1 , Tg2 , Ta , Tw )
and parameters (Rh , Rwire , ), namely:
h = h(V, Ts , Tg1 , Tg2 , Ta , Tw ; Rh , Rwire , ).
(3.11)
These independent quantities can be organized in a vector, namely:
q = {V, Ts , Tg1 , Tg2 , Ta , Tw ; Rh , Rwire , },
(3.12)
where qi ∈ q denotes the generic i-th quantity. The type B standard
uncertainty (coverage factor: 2) of the quantity h, namely Σh,B , can be
computed by the following uncertainty estimation method [85]:
Σh,B
v
u 9 2
X
1u
∂h
= t
Σq i
,
h i=1
∂qi
(3.13)
37
3. Experimental rig: a purposely developed heat flux sensor
where Σqi is the standard uncertainty for the quantity qi . Instead of assuming the nominal value of Rh (namely 26.5 Ω), the value of the sample resistance has been measured as function of the sample temperature
(thermal drift), in order to obtain the functional dependence Rh = f (Ts ).
Hence Eqs. (3.9) and (3.10) are based on the measured potential difference only. The standard uncertainty of the voltage measured by the
multimeter can be assumed ΣV =0.0016 V . The temperatures Ts , Tg1
and Tg2 are critical and, therefore, thermocouples calibrated by thermostatic bath were used. The corresponding uncertainties can be assumed
ΣTs = ΣTg1 = ΣTg2 = 0.05 K. On the other hand, other thermocouples
might be characterized by ΣTa = ΣTw = 0.4 K, because of the intrinsic
uncertainties of the installation setup. ΣRh = ΣRwire = 0.014Ω has been
chosen. Anemometer calibration has been performed and corresponding
uncertainty has been calculated. The latter depends on measured velocity
according to a polynomial function. Minimum and maximum calculated
values of uncertainty Σvax are 0.1 m/s and 0.38 m/s respectively.
The estimate of the sample surface emissivity requires more care, and
the following procedure is adopted. The sample temperature was measured first by the calibrated thermocouple. Next, the surface emissivity
was tuned by a thermal camera (NEC TH9100 Series Infrared Thermal
Imaging Camera), in order to match the latter (independently) measured
temperature. This procedure provided = 0.23 and 0.1 for copper and
aluminum alloy AlSi10Mg, respectively (below the reason for characterizing also AlSi10Mg is clarified). A quite large value of uncertainty has
been assumed, i.e. Σ = 0.1, owing to the poor quality of the infrared
image. In table 3.1, uncertainties of measured quantities and sensitivities
of measurement devices used in this work are reported.
Using the above values of standard uncertainties Σqi , type B uncertainty
Σh,B has been calculated through Eq. (3.13); Consequently, the type B
relative standard uncertainty σh,B has been calculated by σh,B = Σh,B /hF ,
where hF is a power-law least squares fitting of the experimental data for
each sample. In particular, hF = hF (vav ) = d1 vav d2 , where d1 and d2 are
proper fitting parameters.
On the other hand, a novel method has been proposed here for calculating type A uncertainties. This method aims to take advantage of measurements performed at different velocities to properly calculate tolerance
intervals [4]. Given a set of n measurements of convective heat transfer
coefficients hi , performed at different velocities vi , the latter have been
normalized with regards to the corresponding power-law fitting, namely
38
3.4. Experimental rig description
Table 3.1: measured quantities uncertainties and measurement devices
sensitivities (see Ref. [4]).
Measured quantity
V
Ts
Tg1
Tg2
Ta
Tw
Rh
Rwire
vax
Σqi
0.0016 V
0.05 K
0.05 K
0.05 K
0.4 K
0.4 K
0.014 Ω
0.014 Ω
0.1
0.1−0.38 m/s
Device
Multimeter
Thermocouple
Thermocouple
Thermocouple
Thermocouple
Thermocouple
Multimeter
Multimeter
Thermal camera
Vane anemometer
Sensitivity
0.00001 V
0.041 mV /K
0.041 mV /K
0.041 mV /K
0.041 mV /K
0.041 mV /K
0.0001 Ω
0.0001 Ω
0.08 K
0.1 m/s
h0i = hi /hF (vi ). Consequently, a new set composed by n elements h0i ,
distributed according a Gaussian function, has been obtained. Hence, the
mean value µ0 and the standard deviation σ 0 of the latter set can be computed. Finally, the population mean µ and the maximum population standard deviation σ of the set can be calculated by the Student’s t-distribution
and the Chi-squared distribution,
respectively. In√particular, µ = µ0 ± σµ ,
√
0
where σµ = t1−α/2, n−1 σ / n and σ = σ 0 /χα/2 n − 1 [85]. Combining
q
the previous standard deviations, namely σh,A = σµ2 + σ 2 , it results
σh,A
v
u 2
ut
n−1
0 t 1−α/2, n−1
+ 2 .
=σ
n
χα/2
(3.14)
Finally, the overall relative standard uncertainty can be obtained as
q
2
2 .
σh = σh,A
+ σh,B
(3.15)
It is worth to highlight that the previous procedure allows one to compute tolerance intervals, which are wider than confidence intervals, and
more robustly estimate the experimental uncertainty. Anticipating the
experimental results described in Section 3.5, the maximum and mean relative uncertainty for the convective heat transfer coefficient is ±9.9% and
±6.7%, respectively. Moreover, in these experiments, A-type uncertainty
39
3. Experimental rig: a purposely developed heat flux sensor
is wider than B-type uncertainty (the latter being ±2%), proving that the
overall accuracy of the measurement procedure is satisfactory.
Values of type A uncertainties depend on the number of experimental
tests n (See Eq. 3.14). In particular, they are supposed to decrease as
n increases (See Ref. [4]). Finally, a comprehensive statistical analysis of
experimental data must include a procedure able to detect outliers in the
data sets. In this study Grubb’s test has been used to identify outliers
among extreme data. For these particular data sets no outliers have been
found, hence no data have been canceled out. The latter result proves
good repeatability of the proposed sensor and experimental rig.
3.5. Experimental rig validation
In this section, experimental results are reported in order to validate the
proposed sensor and experimental rig. In particular, 15 and 13 experimental points were investigated for aluminum alloy AlSi10Mg and copper
samples smooth surfaces respectively, by varying the axial velocity in the
range 3.1−15.5 m/s. A sample made of AlSi10Mg has been tested in
order to make sure that the proposed sensor can properly function with
samples made of a different material compared to the guard. In particular, AlSi10Mg has a thermal conductivity of 150 W/m/K, which is
roughly one-third compared to copper, and is often used in DLMS application [3]. Experimental points are reported in Tables 3.2 and 3.3.
The sample heater thermal power in the proposed experiments is roughly
0.126 W (corresponding to power densities of 0.102 W/cm2 ). The power
densities are quite small (due to air), which make accurate measurement
pretty challenging. For each test, the thermal power supplied to the guard
is adjusted in order to satisfy the following condition at steady state:
Ts = (Tg1 + Tg2 )/2. During tests, the thermal balance was found to be
well satisfied: For the upstream part of the guard, the average temperature
difference Tg1 − Ts is 0.19 K (maximum 0.40 K) while, for the downstream
part, the average temperature difference Ts − Tg2 is 0.23 K (maximum
0.40 K).
Experimental data are reported in Fig. 3.5, where they are compared
to both an experimental correlation from literature [8] (with conduction
losses properly taken into account by Eq. (3.8)) and numerical results
from CFD model (see the Appendix A for details). As visible in Fig. 3.5,
the accordance of experimental results with the two chosen benchmarks is
40
3.5. Experimental rig validation
Table 3.2: Experimental data about convective heat transfer for AlSi10Mg
sample (see Ref. [4]).
v
[m
s ]
3.3
4.2
5.2
6.2
7.2
8.2
9.2
9.2
10.3
10.3
11.3
12.2
13.2
14.2
15.1
ReL
[−]
3493
4528
5585
6659
7747
8843
9944
9944
11159
11159
12263
13256
14357
15454
16549
Ts
[℃]
61.9
57.9
54.0
51.1
48.0
46.7
45.0
44.0
43.2
43.4
42.2
41.1
40.1
39.4
38.9
Ta
[℃]
29.2
29.1
29.0
29.3
28.7
28.2
27.5
27.3
27.3
27.7
27.3
27.3
27.2
27.3
27.3
Vh2
Rh
[W ]
0.1271
0.1271
0.1270
0.1270
0.1270
0.1270
0.1269
0.1275
0.1274
0.1273
0.1274
0.1273
0.1273
0.1273
0.1274
h
[ mW
2K ]
30.80
35.10
40.58
46.75
52.67
54.95
58.08
60.96
64.24
65.00
68.85
74.19
79.07
84.75
88.97
N uL
P r 1/3
[−]
26.47
30.17
34.88
40.17
45.27
47.23
49.91
52.39
55.21
55.86
59.17
63.76
67.96
72.83
76.47
σh
[%]
6.55
5.97
5.48
5.14
4.88
4.79
4.69
4.65
4.59
4.58
4.52
4.46
4.42
4.38
4.36
41
3. Experimental rig: a purposely developed heat flux sensor
Table 3.3: Experimental data about convective heat transfer for copper
sample (see Ref. [4]).
v
[m
s ]
3.1
3.3
3.8
4.8
6.3
8.8
8.8
10.1
12.2
13.0
14.1
14.9
15.1
ReL
[−]
3289
3493
4111
5160
6768
9503
9503
10938
13256
14137
15345
16330
16549
Ts
[℃]
62.0
62.7
58.0
52.0
48.5
42.5
44.5
42.6
40.2
39.6
39.1
39.3
37.3
Ta
[℃]
29.2
29.1
29.3
27.4
27.9
27.2
28.6
27.5
26.9
27.1
27.1
28.4
26.3
Vh2
Rh
[W ]
0.1248
0.1259
0.1241
0.1253
0.1254
0.1261
0.1253
0.1244
0.1254
0.1255
0.1257
0.1251
0.1264
h
[ mW
2K ]
28.74
28.23
33.63
38.94
47.48
64.70
62.16
64.93
74.70
79.84
83.01
91.99
91.68
N uL
P r 1/3
[−]
24.70
24.26
28.90
33.47
40.80
55.61
53.42
55.81
64.20
68.62
71.34
79.06
78.79
σh
[%]
8.42
8.50
8.32
8.63
9.33
8.55
8.79
9.77
8.54
8.58
9.85
8.52
8.30
good. Maximum and average deviations from CFD model are 13.7% and
6.3%, respectively, whereas the same devations with respect to literature
[8] are 10.7% and 3.4%, respectively. The results of copper and aluminum
alloy are consistent, showing that the proposed sensor can operate with
samples made of different materials (as long as the thermal conductivity
is high enough to ensure a uniform temperature field).
In Fig. 3.6, are reported the result of additional experimental tests, where
the power supplied to the sample is the varying parameter, in order to
understand the optimal heat flux for the measurement. In this case, flow
velocity equal to 3.4 m/s at the channel axis is kept fixed. Standard
theoretical arguments require that a variation of the supplied power should
not affect the value of the convective heat transfer coefficient, meaning that
the supplied power is expected to show a linear behavior with respect to
temperature difference.
This is confirmed in Fig. 3.6, where a linear best fit reveals a positive
supplied power for a null temperature rise, defined as the difference between the temperature of the sample and that of air: Ts − Ta . However,
we would expect that such a linear correlation passes through the origin of
axes (i.e. no temperature difference is observed when the power supplier is
42
3.5. Experimental rig validation
90
80
60
L
Nu /Pr0.33
70
50
40
Al
Cu
Maddox&Mudawar (1989)
CFD
30
20
0.5
1
ReL
1.5
2
4
x 10
Figure 3.5: Comparison between experimental data, Maddox&Mudawar
experimental correlation[8] and CFD model for aluminum alloy
and copper smooth surface (see Ref. [4]).
off). This evidence can be explained as follows. All the measurements are
based on the air temperature at the channel axis, see Eq. (3.9). However,
in the present case, there is a small temperature difference between the air
flowing inside the wind tunnel and the environment, because of the irreversibilities caused by the blower. The blower increases air temperature of
roughly 2 K, and this generates a temperature difference between air and
the channel walls. While air flows through the channel, the portion of air
flushing close to the walls is cooled down by the walls. On the contrary,
the air flowing at the channel axis experiences a weaker cooling. At the
test section, the air thermal profile is slightly non-uniform: namely, air
temperature at channel axis is slightly higher than the temperature of air
flushing on the sample. When the latter is at the same temperature of the
air flowing at the channel axis (the difference Ts −Ta = 0 K), the sample is
warmer than air passing in its close proximity and a small thermal power
removal is observed (See Fig. 3.6).
43
3. Experimental rig: a purposely developed heat flux sensor
Al
Cu
Al linear fitting
Cu linear fitting
Q [W]
0.1
0.05
0
0
10
20
Ts-Ta [K]
30
40
Figure 3.6: Linear correlation between power given to the sample and temperature difference between sample and air, for a constant air
velocity (see Ref. [4]).
Now the experimental data shown in Table 3.2 and 3.3 are examined, in
order to estimate how much this phenomenon affects the measurements
reliability. At the test section, the temperature difference between air and
walls is highly variable, with a maximum recorded value of 1.78 K and
a minimum one of 0.16 K. This means that slightly different thermal
boundary layers showed up at the test section during the experimental
campaign. This fact may have an effect on the measurement of the average
convective heat transfer, as it is directly influencing the considered Ta at
the denominator of Eq. (3.9). Instead of using the air temperature at the
channel axis, i.e. Ta , one could use a proper corrected value, namely the
adiabatic mixing temperature Tm , in Eq. (3.9), taking into account the
actual temperature profile. For each experimental data shown in Table
3.2 and 3.3, one could estimate two values of h by setting Tm = Ta (thus
obtaining the value of h shown in Fig. 3.5) or Tm = Tw . Calculating the
relative errors, defined as the differences between the h values calculated
using Tm = Ta and the h values calculated using Tm = Tw , a maximum
and an average relative error equal to ±2.6% and ±1.5% has been found,
respectively. The latter values are much smaller than the estimated overall
measurement uncertainties, namely ±9.9% and ±6.7%. Hence it is possible
44
3.6. Discussion
to assume that the above phenomenon has a negligible effect for value of
the heat flux equals or higher than those used in these experiments (i.e.
Q ≥ 0.126 W ), corresponding to a power density of ≥ 0.102 W/cm2 . The
present release of the sensor works in range of 0.102−3.100 W/cm2 , where
the maximum power density depends on the adopted heater. Maximum
working temperatures are also estimated to be equal to 50−100 Celsius for
previous power densities. It is worth to point out that the above maximum
working temperature and power density are mainly limited by the chosen
heater, as well as by the present selection of materials. These thresholds
can be easily overcome by proper design choices, without changing the
main idea of the proposed sensor.
3.6. Discussion
In the present Chapter the experimental rig, used to characterize convective heat transfer coefficient of high efficient surfaces and devices proposed
in the following of this work, has been described. In particular, design and
validation of a purposely developed sensor for measuring convective heat
flows is described in details. The key idea is to exploit the notion of thermal
guard in order to significantly reduce the effects of spreading heat conduction losses. The maximum and mean estimated relative uncertainties for
the convective heat transfer coefficient are found to be ±9.9% and ±6.7%,
respectively. The experimental results are found to be in good agreement
with both experimental data from the literature and a purposely developed
computational fluid dynamic model. Maximum and average deviations of
the measured Nusselt number from the estimated value by the numerical model are 13.7% and 6.3%, respectively. The comparison of reported
measurement with literature [8] is even more satisfactory: Maximum and
average deviations of NuL are found to be 10.7% and 3.4%, respectively.
The evidence that uncertainties due to (spreading) conduction losses can
be effectively reduced by the thermal guard implies that no numerical
model is required to post-process the measured quantities, and this leads
to a direct measurement technique. The experimental rig can cope with
quite small thermal fluxes (i.e. < 0.2 W/cm2 ), thus enabling the study of
convective heat transfer enhancement methodologies in forced air (specific
thermal fluxes here are order of magnitudes smaller than the one measured
in [8]).
45
3. Experimental rig: a purposely developed heat flux sensor
In the next Chapter, micro-pin fins arranged in regular patterns are investigated as a heat transfer enhancement technique. The aim is to develop
a novel optimization method, suited for ”not subtractive” manufacturing
technologies, devoted to design cost-effective heat transfer solutions. A
certain number of configurations is experimentally characterized using the
test rig described here. Such a long-lasting investigation necessarily require
a purposely dedicated experimental bench for thermal characterization.
46
4. Patterns of micro-protrusions
for enhanced convective heat
transfer
In Chapter 3, the design of a purposely dedicated experimental rig has
been presented. This has been developed in order to characterize thermal performances of high efficiency heat transfer surfaces and devices.
In the present Chapter, this experimental rig is used to investigate patterns of diamond shaped, micro-pin fins (i.e. patterns of micro-protrusions
or micro-protruded patterns) on flush mounted heat sinks for convective
heat transfer enhancement. The role played by geometrical parameters
and fluid-dynamic scales are discussed, and novel findings are pointed out.
Moreover, a novel methodology specifically suited for micro-protruded patterns thermal optimization is designed, leading to 73 % enhancement in
thermal performance respect to commercially available heat sinks, at fixed
costs. Such a methodology is tailored to deal with devices fabricated by
”not subtractive” manufacturing technologies, e.g. Additive Manufacturing (AM). Contents of this Chapter can be also found in [7].
4.1. Motivations
This Chapter focuses on diamond shaped micro-protruded patterns, which
are investigated as a promising method to enhance heat transfer performances of flush mounted heat sinks.
More specifically, a systematic
procedure based on design of experiments approach is proposed to:
• Investigate the convective heat transfer phenomenon, in order to understand, interpret and describe the effect of geometrical parameters
and fluid-dynamic scales on heat transfer;
47
4. Patterns of micro-protrusions for enhanced convective heat transfer
• Design a novel methodology suitable for a reliable and automatic
thermal optimization of micro-protruded patterns fabricated by ”not
subtractive” techniques (e.g. AM).
The Chapter is organized as follows. In Section 4.2, different diamond
protruded patterns are rationally designed by taking advantage of the design of experiments approach. In Section 4.3, the results of experimental
characterization are reported and a mathematical model describing the
influence of geometrical parameters and flow regimes on thermal transmittance of diamond protruded patterns is developed. In Section 4.4, the
thermal fluid-dynamics features of diamond micro-protruded patterns for
heat sinks are discussed. Optimization methodology is proposed in Section
4.5. Finally, in Section 4.6, results are discussed.
4.2. Design of experiments
To obtain an independent benchmark of data, nine copper samples, each
characterized by a peculiar Diamond micro-Protruded Pattern (DPP), are
designed and manufactured by milling. The convective heat transfer coefficient for each sample is measured. The bottom part of each sample
consists in a parallelepiped block (11.1 x 11.1 x 5 mm3 ), which can be
mounted in the experimental test bench described in Chapter 3. Samples
are characterized by diamond micro-protrusions, which are arranged in a
regular pattern. Each diamond shaped micro-protrusion is a parallelepiped
pin, with a d x d square section rotated by 45 degrees with respect to the
main flow direction. Protrusions are arranged according to a staggered
configuration, as represented in Fig. 4.1.
A DPP is fully determined by 3 geometrical independent degrees of freedom (DoF). There are no constrains in choosing the DoF to use for the
design, except for their property of independence. As an example, given
the height of the protrusion H, the base edge of the protrusion d, the
pitch between neighboring protrusions p (see Fig. 4.1), the number of
protrusions N and s = p − d, a possible choice for the 3 DoF could be
{H, p, d}. However, the use of dimensionless parameters is preferable, as
they typically ensure a wider generality of results.
In previous studies on heat transfer through protruded patterns, the ratios between characteristic geometrical lengths have been adopted as governing parameters for the measured thermal performances. For example,
Garimella et al. [34] chose the ratios between (i) spacing and protrusions
48
4.2. Design of experiments
height and (ii) channel height and protrusions height as significant parameters for characterizing heat transfer phenomenon in arrays of protruding
elements. Leung et al [86], instead, chose the ratio between base length
and height of protrusions, as well as the ratio between channel height and
protrusions height as characterizing parameters.
Figure 4.1: Sample geometry: Isometric view on left-hand side; Top view
on right-hand side (See Ref. [7]).
In this work, to design the test matrix, a novel set of geometrical dimensionless parameters is considered. The investigation of those specific
parameters is proved to be suitable in developing a novel methodology for
the thermal optimization of micro-protruded patterns for heat sinks. In
this context, the optimal configuration is the one ensuring the maximum
thermal transmittance, at fixed amount of material needed to manufacture
the micro-protrusions. In fact, the amount of used material is a suitable
production cost indicator for most of the ”not subtractive” manufacturing
technologies, both traditional (e.g. extrusion) and innovative (e.g. additive
manufacturing) ones. In other words, optimal configuration is intended to
be the one that guarantees the maximum thermal performance per unit of
production costs. Parameters investigated in this study are:
• Plane solidity (or plan area density) λp , defined as the fraction of
the root surface area (i.e. in our case An = 11.12 mm2 = 123 mm2 )
covered by protrusions (see Fig. 4.1, top view). This parameter
expresses the pattern density, and it ranges from 0 to 1; Low values of
λp refer to sparse patterns, whilst high values denote dense patterns
49
4. Patterns of micro-protrusions for enhanced convective heat transfer
(see also Fig. 2 in ref. [87]).
• Enhancement ratio in convective heat transfer surface area A/An ,
where A is the sample area, which is defined as the sum of root
surface area and protrusions surface area, namely A = An + 4dHN .
• Dimensionless mixed length V /(AY0 ), where V = N Hd2 is the volume of the micro-protrusions and Y0 = 0.0503 mm is the average
viscous length (or average wall unit [88]), which is calculated as the
mean viscous length over the range of fluid flows (i.e. Reynolds numbers) investigated in this study. The dimensionless mixed length is
obtained as a ratio between geometric (V /A) and fluid-dynamic (Y0 )
lengths. In particular, V /A represents the ratio between the amount
of material for manufacturing the protrusions (i.e. production cost
indicator) and the available surface area involved in the heat transfer phenomenon, while Y0 is strictly related to the boundary layer
thickness.
Comparing geometric and fluid-dynamics scales is essential to understand
their interactions, as well as to determine how the optimal geometrical
DPP configuration depends on the flow field. It is worth to mention that
V /(AY0 ) is not the only mixed length analyzed in this study. In the following, the importance of the dimensionless protrusion height H/Y0 is also
discussed. This parameter represents the ratio between protrusion height
and boundary layer thickness, and it quantifies the penetration of protrusions into the boundary layer. In the following, we refer to the three
parameters defined above as model parameters, because they are expected
to significantly affect both the thermal transmittance of the heat sink T r
[W/K] and the volume of the micro-protruded pattern, therefore allowing
to define an optimization criteria. λp plays a key role on the interactions between thermal fluid-dynamics structures (i.e. eddies, boundary
layers, etc.) and micro-structures, thus strongly affecting the convective
heat transfer coefficient h [W/m2 /K]. For instance, λp is often used to
study the interactions between buildings and the atmospheric boundary
layer [87] , but it has been demonstrated to be very effective in describing
interactions between fluid-dynamics structures and micro-structures in a
macroscopic channel too [3]. The A/An parameter is considered because
heat flux, thus T r, is strongly affected by the surface area involved in the
heat transfer phenomenon. Since these two parameters are not directly
linked to the production cost parameter (V ), a third parameter V /(AY0 )
is also included.
50
4.2. Design of experiments
The three model parameter described above can be expressed as function
of the geometrical parameters {H, p, d} as:
d2
N d2
= 2,
An
p
(4.1)
A
4dH
= 2 + 1,
An
p
(4.2)
V
Hd2
.
=
AY0
Y0 (4dH + p2 )
(4.3)
λp =
These equations are valid under the assumption that the number of protrusions N can be expressed as:
N=
An
.
p2
Obviously, the model parameters have a physical meaning only if:

 0 < λp < 1,
A/An > 1,

V /(AY0 ) > 0.
(4.4)
(4.5)
Any existing
DPP is
n
o fully determined by defining all components of the
A
V
vector λp , An , AY0 . In this study the tested DPPs are designed taking
advantage of the Design Of Experiments (DOE) approach. In particular,
a Taguchi (or L9 orthogonal arrays) based, 3 levels - 3 factors, fractional
DOE is applied [11]. Each parameter (or factor) can assume three possible
values (or levels), namely low (1), medium (2) or high (3), as listed in Table
4.1. Therefore, once the levels per each parameters have been defined, the
geometry of the nine DPPs to be tested is determined according to the
test matrix proposed in ref. [11] and reported in Table 4.2.
Due to the rough tolerances of the milling process, the actual parameters
of the samples are slightly different from the design values reported in
Table 4.1: in Table 4.3, the model parameters and the extra geometrical
quantities are reported for each sample. Fig. 4.2 shows how all samples
are located in the parameter space; whereas Fig. 4.3 reports the pictures
of the analyzed samples.
51
4. Patterns of micro-protrusions for enhanced convective heat transfer
Table 4.1: Design values and associated levels for each model parameter
(See Ref. [7]).
parameter level
1
2
3
λp
0.15
0.35
0.55
A/An
1.5
2.5
3.5
V /(AY0 )
2
2.75
3.5
Table 4.2: Test matrix [11] (See Ref. [7]).
sample
#1
#2
#3
#4
#5
#6
#7
#8
#9
λp level
1
1
1
2
2
3
3
3
2
A/An level
1
2
3
1
2
3
1
2
3
V /(AY0 ) level
1
2
3
2
3
2
3
1
1
It is worth to provide more details on the calculation of Y0 . The average
viscous length Y0 can be defined as:
Y0 =
1
ReD,max − ReD,min
Z
ReD,max
y0 (ReD ) dReD
.
(4.6)
ReD,min
As demonstrated in [3], in case of smooth pipe turbulent flow, viscous
length y0 depends on the hydraulic diameter based Reynolds number
ReD = vD/ν as:
y0 =
ReD
D
p
,
fB /8
−1/4
(4.7)
where fB = fB (ReD ) = 0.3164 ReD
is the friction factor expressed by
the phenomenological correlation proposed by Blasius [89], v is the average
fluid velocity, D is the hydraulic diameter, and ν is the fluid kinematic
viscosity.
52
4.3. Experimental characterization and data reduction
Table 4.3: Values of model parameters and extra geometrical quantities for
the tested samples (See Ref. [7]).
Sample
#1
#2
#3
#4
#5
#6
#7
#8
#9
λp
0.15
0.15
0.13
0.28
0.28
0.44
0.52
0.37
0.26
A/An
1.52
2.57
3.12
1.47
2.52
3.28
1.49
2.32
3.71
4
V /(AY0 )
2.04
2.99
3.55
2.55
3.60
2.76
3.60
2.21
1.85
H [mm]
1.03
2.45
4.78
0.70
1.56
1.05
0.55
0.56
1.16
V/(AY0) low
n
A/A
2
V/(AY0)
V/(AY0) high
p [mm]
3.08
2.62
2.90
3.00
2.28
1.20
3.20
1.10
1.02
s [mm]
1.88
1.62
1.85
1.40
1.08
0.40
0.90
0.43
0.50
4
λ low
3.5
λP mid
3
λP high
P
V/(AY0) mid
3
d [mm]
1.20
1.00
1.05
1.60
1.20
0.80
2.30
0.67
0.52
2.5
2
1
0.2 λ 0.4
P
(a)
0.6
1.5
1
2
A/An
3
4
(b)
Figure 4.2: Collocation of samples in the model parameter space. Due
to manufacturing tolerances, a non uniform sampling of the
parameter space is considered (See Ref. [7]).
4.3. Experimental characterization and data
reduction
In this section, the experimental thermal characterization of all samples is
provided. Moreover, the experimental results are compared to the model
obtained by data reduction analysis.
53
4. Patterns of micro-protrusions for enhanced convective heat transfer
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
Figure 4.3: Tested samples (See Ref. [7]).
Experimental characterization has been carried on by the experimental
rig described in Chapter 3. Heat transfer performance of each sample is
reported as function of the heated edge, average velocity based Reynolds
number ReL = vL/ν,, defined in Chapter 3.
In Fig. 4.4, the convective heat transfer coefficient of all samples is reported
in terms of N uL /P r0.33 , where N uL and P r are respectively the dimensionless Nusselt and Prandtl numbers, defined in Chapter 3. In Fig. 4.5,
thermal transmittances T r = hA of samples are shown. In both Fig. 4.4
and Fig. 4.5, the experimental characterization of a reference flat sample
(i.e. without protrusion) is reported. The model is obtained by data reduction analysis discussed in the following. Finally, in Fig. 4.6, the results in
54
4.3. Experimental characterization and data reduction
terms of quantity T r/V are reported. Error bars reported in Figs. 4.4, 4.5,
4.6 are estimated according to the methodology discussed in Chapter 3. It
is worth to mention samples, with the same protruded patterns presented
in Section 4.2, have been also fabricated by direct metal laser sintering
(DMLS). Preliminary experiments, aiming to characterize these samples,
revealed thermal performance of each sample by DMLS was similar than
counterpart by milling. Hence the complete experimental characterization
has been carried on for milled samples only.
200
1
2
3
4
5
6
7
8
9
Flat
NuL/Pr0.33
150
100
50
0
0
0.5
1
ReL
1.5
2
4
x 10
Figure 4.4: Comparison between experimental (symbols) and model (solid
lines) results in terms of N uL /P r0.33 (See Ref. [7]).
In the following, a model able to predict the convective thermal transmittance
of ao generic DPP heat sink as a function of model parameters
n
A
V
λp , An , AY
and fluid flow regime, namely ReL , is presented. The model
0
is based on data reduction on the experimental measurements of T r. A
reference Reynolds number is defined:
ReL,R = 104 ,
(4.8)
while T r is modeled as the product of two functions:
55
4. Patterns of micro-protrusions for enhanced convective heat transfer
0.1
1
2
3
4
5
6
7
8
9
Flat
Tr [W/K]
0.08
0.06
0.04
0.02
0
0
0.5
1
Re
1.5
2
4
L
x 10
Figure 4.5: Comparison between experimental (symbols) and model (solid
lines) results in terms of T r (See Ref. [7]).
T r = gT rR .
(4.9)
In Eq. 4.9, T rR is the transmittance value at the reference n
Reynolds numo
V
ber, which is expected to depend on the model parameters λp , AAn , AY
.
0
On the other hand, g accounts for thermal transmittance as we move
away from
the reference
flow regime, and it is modeled as a function of
H
H
A
V
=
λ
,
,
and Reynolds number ratio ReL /ReL,R .
p An AY0
Y0
Y0
0
0
The quantity T rR can be split into T rR = T rR
+ ∆T rR , where T rR
is
the transmittance of flat surface at the reference Reynolds number, while
∆T rR is the additional transmittance due to the presence of DPP on the
heat sink. Consequently, T rR can be modeled as:
0
T rR = T rR
+V
∆T rR
.
V
(4.10)
In this form, V represents the amount of additional raw material needed to
manufacture the protruded pattern, while the parameter ∆TVrR represents
the enhancement in thermal transmittance of the device achieved per unit
volume. ∆TVrR is modeled by a second order polynomial function as:
56
4.3. Experimental characterization and data reduction
-3
Tr/V [W/K/mm3]
1.5 x 10
1
2
3
4
5
6
7
8
9
1
0.5
0
0
0.5
1
ReL
1.5
2
4
x 10
Figure 4.6: Comparison between experimental (symbols) and model (solid
lines) results in terms of T r/V (See Ref. [7]).
2
2
d
d
d
d
2
∆T rR
cp + c2 A + c3 V + c4 λ
cp + c5 A + c6 V
= c1 λ
V
An
AY0
An
AY0
d
d
d
d
A
V
A
V
cp
cp
+c7 λ
+ c8 λ
+ c9
.
An
AY0
An AY0
(4.11)
where the superscript b indicates the normalized model parameters, obtained as:

cp = λp ,

λ

(λp )Avr






A
 c
An
A
,
An = ( A )
An Avr





V


AY
d
V

 AY0 = V 0 ,
AY0
Avr
1
9
(λp )Avr =
A
An
P9
=
Avr
V
AY0
i=1
1
9
P9
=
Avr
(λp )i
i=1
1
9
P9
A
An
i=1
(4.12)
i
V
AY0
i
57
4. Patterns of micro-protrusions for enhanced convective heat transfer
Subscript i in equation above denotes the i-th sample.
The vector {C} ={c1 , c2 , c3 , c4 , c5 , c6 , c7 , c8 , c9 } collects all the model
coefficients, which are obtained by a regression procedure from the experimental data (see Appendix B for further details). In particular, from the
data regression, c1 = −0.0003, c2 = +0.0010, c3 = −0.0003, c4 = −0.0013,
c5 = −0.0011, c6 = −0.0073, c7 = −0.0041, c8 = +0.0067, c9 = +0.0076
are obtained.
The function g =
Tr
T rR
is modeled as:
g=
where B = B
H
Y0
ReL
ReL,R
B
=
ReL
104
B
,
(4.13)
is computed as:
B = log ReL
104
Tr
.
T rR
(4.14)
From the tested samples, ten experimental values of B are available for data
regression. Considering a least mean squares fitting procedure, results are
best fitted by:
d2
H
H
exp −d3
+ d4 ,
(4.15)
B = d1
Y0
Y0
where the fitting parameters d1 , d2 , d3 , d4 assume the values 0.003316,
2.3, 0.1039 and 0.66, respectively. In Fig. 4.7, the comparison between
experimental values of B and the corresponding analytical model described
by Eq. 4.15 is shown.
The proposed model reveals an excellent agreement with experimental
data, as shown in Figs. 4.4, 4.5, 4.6.
58
4.4. Thermal fluid-dynamics features of micro-protruded patterns
Figure 4.7: Comparison between experimental values of B and the best
fitted analytical model (See Ref. [7]).
Finally, dimensionless fin parameter ml is introduced, where l is the protrusion height H defined in Table 4.3, and m is defined as [38]:
0.5
4h
m=
,
(4.16)
λCu d
where λCu = 388 W/m/K is the thermal conductivity of copper.
4.4. Thermal fluid-dynamics features of
micro-protruded patterns
In the following, the experimental results presented in Section 4.3 are interpreted, and the main thermal fluid-dynamic features of diamond microprotruded patterns discussed.
Before proceeding further, it is worth of note that the fin efficiency plays
negligible role in convective heat transfer of the considered diamond microprotruded patterns. In fact, here the temperature gradient along the protrusions length is very small. To prove this, for each protrusion ml is
59
4. Patterns of micro-protrusions for enhanced convective heat transfer
calculated by Eq. 4.16 considering h = hmax = 200 W/m2 /K, i.e. the
maximum convective heat transfer coefficient experimentally measured.
As a result, the fin efficiency is higher than 98 % in all the considered
samples, hence its effect is negligible.
The parameter λp plays a key role in controlling the condition of fluid
stagnation and, consequently, the convective heat transfer coefficient. As
shown in Fig. 4.4, samples characterized by low λp (i.e. #1, #2 and #3)
experience larger values of N uL /P r0.33 than samples with higher λp (i.e.
#6, #7, #8 and #9). Focusing on sparse patterns (low λp ) it can be
noticed that H significantly influences N uL /P r0.33 , which monotonically
increases with H. This is due to the fact that higher protrusions are able
to penetrate deeper in the fluid boundary layer, hence they are flushed
by stronger flow field (see Fig. 4.4). This phenomenon allows to achieve
a huge increase in convective heat transfer: the sample with the highest protrusions (sample #3) experiences an enhancement in N uL /P r0.33 ,
almost constant over the entire range of ReL under study, up to 150 %
as compared to flat surfaces, while T r increases up to 700 %. On the
other hand, by increasing the density of patterns (i.e. increasing λp ), fluid
stagnation takes place and consequently N uL /P r0.33 decreases. In particular, very high density patterns, can experience values of N uL /P r0.33
even lower than flat surface (see sample #6, #7, #8 and #9). In Fig. 4.8,
the influence of λp on N uL /P r0.33 is shown. Here, a comparison of nine
experimental points with an exponential-based fitting curve is reported.
This clearly demonstrates that λp plays a significant role: N uL /P r0.33
monotonically decreases with increasing λp , even though this result is limited to the range of λp considered in this work. The latter experimental
evidence underlay a phenomenon very similar to the one of bypass flow experienced by unshrouded heat sinks and described in Section 2.2: If heat
sink package became too dense (i.e. λp increases) air flows avoid to pass
through fins (i.e. protrusions), resolving in a reduction of convective heat
transfer.
In all the tested samples, H/Y0 plays a key role in determining how the
fluid flow regime, i.e. ReL , influences the thermal transmittance. In particular, Fig. 4.7 suggests that an optimal value of H/Y0 exists, which lies in
the range 10 < H/y0 < 40, where protrusions are at least twice the viscous
sub-layer height (≈ 5 y0 according [88]), but still short enough to remain
in the viscous wall region (≤ 50 y0 according [88]). Being y0 inversely proportional to the Reynolds number (according Eq. 4.7) the optimal height
H is expected to be function (monotonically decreasing) of the Reynolds
number too. This is confirmed by experimental results: Being TVr the pa-
60
4.5. Optimization methodology for micro-protruded patterns
200
Experiment
Fitting
L
R
Nu /Pr0.33
150
100
50
0
0.1
0.2
0.3 λ
0.4
0.5
0.6
p
Figure 4.8: Influence of λp on N uL /P r0.33 (See Ref. [7]).
rameter to maximize, and focusing on the three samples characterized by
the lowest values of λp (hence the highest convective heat transfer coefficient), it could be noticed in Fig. 4.6 that in the low Reynolds number
range (0.3 × 104 < ReL < 0.9 × 104 ) the sample #3 (with the highest value
of H), experiences the highest TVr . In the intermediate Reynolds number
range (0.9 × 104 < ReL < 1.4 × 104 ), the sample #2 (with the intermediate H, among the three ones) experiences the highest TVr . Finally, in the
high Reynolds number range (1.4 × 104 < ReL < 1.7 × 104 ), the sample
#1 (with the lowest H) experiences the highest TVr . Consequently, The
optimal configuration depends on ReL .
4.5. Optimization methodology for
micro-protruded patterns
In this section, an automatic methodology for thermal optimization of
diamond micro-protruded patterns for heat sinks is presented. In addition,
the algorithm is implemented and applied to a real case study and results
are reported and discussed.
61
4. Patterns of micro-protrusions for enhanced convective heat transfer
Input parameters of the algorithm are the heat sink working conditions,
namely Reynolds number ReL,W , heat flux to be removed QW and the
temperature difference between heat sink and cooling fluid ∆TW . As a
result, the automatic optimization
algorithm provides geometrical configo
n
V
A
urations, (in terms of λp , An , AY0 or equivalently {H, d, p}) that maximize T VrW (namely the thermal transmittance per unit of production cost),
QW
while guarantee T r = T rW = ∆T
.
W
The proposed algorithm
o the possible configurations, i.e. pan considers all
V
A
rameter combinations λp , An , AY0 , within the parameter range investigated by experiments (where data regression is proved to be valid). For
each configuration, the algorithm calculates the corresponding values of V
and T r through the model provided by data regression (Eq. 4.9). Among
all the possible configurations, the algorithm retains the ones that guarantee T r = T rW and discard the others. Finally, among the retained configurations, the one characterized by the minimum value of V is chosen. In
particular, the parameter space (i.e. the possible DPP configurations) is
numerically explored as follows: Each parameter can assumes 20 possible
discrete values, by uniformly partitioning the parameter range. Then, the
algorithm calculates the value of T r associated to each of the 203 = 8000
possible DPP configurations (i.e. possible combination of the 3 model parameters). T rW is compared to the value of T r for each configuration, and
configurations that match T rW with a tolerance of 5% are retained.
As discussed in section 2.4 heat transfer devices typically includes both
thermal transmittances and pressure losses, hence optimization problems
usually deal with efficiency parameters that consider both the aforementioned phenomena, e.g. aerothermal efficiency ηA defined in Section 2.4.
In this work, the effects of protruded patterns on pressure losses are neglected, because this study is focused on applications where these effects
are not significant. Nevertheless, it is worth to stress that the methodology
presented in this work could be extended to a more general case, by simply
substituting T VrW (thermal performances per unit of production cost) with
ηA as the parameter to be maximized, as described in Section 2.4
As a real case study, the developed algorithm is used to perform thermal optimization of DPP heat sink, i.e. maximum transmittance per
unit of production costs, for three different Reynolds numbers, namely
ReL = 0.5 × 104 , 104 and 1.5 × 104 , and with a range of transmittance
values: 0.02 < T rW < 0.1 W/K. In Tables 4.4, 4.5, and 4.6 the optimal
geometrical parameters of DPP heat sinks for different T r are reported,
62
4.5. Optimization methodology for micro-protruded patterns
in the case of ReL = 0.5 × 104 , 104 and 1.5 × 104 , respectively. It is
worth of note that for ReL = 0.5 × 104 the maximum transmittance is
T r = 0.045 W/K, because the parameter space explored in the optimization process is limited to the one investigated by experiments. Fig. 4.9
summarizes results of that case study: on the abscissa is reported DPP
volume V , namely the production cost index, while on the ordinate the
maximum (hence optimal) thermal transmittance T rmax achieved for the
three Reynolds numbers under exam is shown. It can be noticed that
the volume, and consequently the production cost of the device, increases
by decreasing ReL (worst convective heat transfer). In Table 4.7 optimal
designs obtained by imposing T rW = 0.03 W/K for the three different
ReL are compared. It is worth of note that optimal values of H chosen
by optimization algorithm are such that the corresponding ratio H/y0 lies
in the range 30 ÷ 35. This result strengthen the hypothesis, exposed in
Section 4.4, of the existence of an optimal value of H/y0 lying in the range
10 < H/y0 < 40. Finally, it is interesting to compare the configurations
obtained from the optimization algorithm with the nine tested samples.
Focusing on reference flow conditions (ReL,R = 104 ), Fig. 4.6 shows that
sample #2 has the best value of transmittance per production costs unit
(i.e. highest T r/V ) among the tested samples, being characterized by
T r = 0.044 W/K and V = 47.7 mm3 . Instead, As shown in Fig. 4.9
and Tab. 4.5, the optimal configuration found by the algorithm allows
to achieve T r = 0.092 with the same amount of material, i.e. at fixed
production costs. Therefore, this example shows that the presented thermal optimization procedure would allow to achieve a 110 % enhancement
in the thermal transmittance of the best performing tested sample, while
keeping production costs unchanged.
63
4. Patterns of micro-protrusions for enhanced convective heat transfer
0.1
4
ReL=0.5x10
4
ReL=10
TrMAX [W/K]
0.08
ReL=1.5x104
0.06
0.04
0.02
0
20
40
V [mm3]
60
Figure 4.9: Case study results: Optimal thermal transmittance versus
DPP volume (See Ref. [7]).
Table 4.4: Optimal design parameters for 0.02 < T r < 0.045 [W/K] and
ReL = 0.5 × 104 (See Ref. [7]).
H
[mm]
1.77
2.03
2.30
2.55
2.81
2.93
64
d
[mm]
0.59
0.64
0.64
0.61
0.58
0.61
p
[mm]
1.64
1.77
1.77
1.69
1.62
1.69
λp
[−]
0.13
0.13
0.13
0.13
0.13
0.13
A
An
V
AY0
[−]
2.55
2.66
2.87
3.18
3.50
3.50
[−]
1.79
1.98
2.07
2.07
2.07
2.17
Tr
[W/K]
0.020
0.026
0.031
0.037
0.042
0.045
V
[mm3 ]
28.31
32.58
36.83
40.88
44.94
46.98
4.5. Optimization methodology for micro-protruded patterns
Table 4.5: Optimal design parameters for 0.02 < T r < 0.1 [W/K] and
ReL = 104 (See Ref. [7]).
H
[mm]
1.18
1.69
2.17
2.55
2.93
3.19
d
[mm]
0.87
0.61
0.57
0.61
0.61
0.66
p
[mm]
2.40
1.69
1.58
1.69
1.69
1.84
λp
[−]
0.13
0.13
0.13
0.13
0.13
0.13
A
An
V
AY0
[−]
1.71
2.45
2.97
3.18
3.50
3.50
[−]
1.79
1.79
1.88
2.07
2.17
2.35
Tr
[W/K]
0.020
0.038
0.056
0.073
0.091
0.100
V
[mm3 ]
19.0
27.1
34.7
40.9
47.0
51.1
Table 4.6: Optimal design parameters for 0.02 < T r < 0.1 [W/K] and
ReL = 1.5 × 104 (See Ref. [7]).
H
[mm]
0.59
1.33
1.62
1.84
2.13
2.24
d
[mm]
1.08
0.75
0.63
0.58
0.53
0.56
p
[mm]
2.25
2.08
1.74
1.60
1.48
1.56
λp
[−]
0.13
0.13
0.13
0.13
0.13
0.13
A
An
V
AY0
[−]
1.50
1.92
2.34
2.66
3.08
3.08
[−]
1.79
1.79
1.79
1.79
1.79
1.88
Tr
[W/K]
0.020
0.038
0.056
0.073
0.091
0.100
V
[mm3 ]
16.6
21.3
26.0
29.5
34.1
35.9
65
4. Patterns of micro-protrusions for enhanced convective heat transfer
Table 4.7: Optimal design parameters for T r = 0.03 W/K at three different Reynolds numbers (See Ref. [7]).
Isometric
view
ReL
[−]
0.5
104
Top view
H
y0
[mm] [mm]
×
104
1.5
104
Side view
×
2.3
H/y0
[−]
0.076
30
1.48 0.041
35
1.07 0.029
36.5
4.6. Discussion
Diamond shaped micro-protruded patterns to enhance convective heat
transfer have been investigated in this Chapter. Two main goals are
achieved:
• The effect of geometrical parameters and fluid-dynamic scales on
convective heat transfer phenomenon are illustrated.
• A methodology suited for the thermal optimization of diamond microprotruded patterns, fabricated by ”not subtractive” techniques (e.g.
AM), is proposed and implemented.
66
4.6. Discussion
Concerning the effect of geometrical parameters and fluid-dynamic scales,
N uL /P r0.33 exhibits a decreasing trend with increasing λp . In particular,
All DPPs characterized by λp > 0.33 clearly show a heat transfer coefficient
lower than the flat case (i.e. no protrusions), due to fluid stagnation.
Concerning sparse patterns (low λp ), it is proved that H plays a key role,
namely the dimensionless group N uL /P r0.33 monotonically increases with
H. In fact, DPP #3, characterized by low λp and the highest H among all
the tested samples, shows the maximum enhancement in N uL /P r0.33 and
T r, up to 150 % and 700 %, respectively. This is due to the fact that high
protrusions are able to penetrate deeper in the fluid boundary layer. On
the other hand, experimental evidence and optimization procedure suggest
the maximum T r/V , i.e. thermal transmittance per unit of production
costs, is reached when H/y0 = 30 ÷ 35.
A novel methodology is developed for thermal optimization of diamond
micro-protruded patterns for heat sinks. An automatic algorithm based on
this methodology is implemented and tested. Provided the heat sink working conditions, an optimization procedure is suggested that calculates the
optimal geometrical configuration ensuring the required thermal performances while maximizing the thermal transmittance per unit of production
costs. Comparing a representative commercial micro-protrusion patterned
heat sink with the optimal configuration determined by the algorithm, the
second achieves an enhance in thermal performance per unit production
cost up to 73% (refer to Appendix C for details). This demonstrates that
the proposed methodology may lead to significant improvement in heat
transfer performances, while keeping unchanged the production costs. The
proposed optimization methodology has rather a general validity, and can
be extended to different micro-protruded or micro-structured patterns, especially if manufactured by ”not subtractive” techniques (e.g. Additive
manufacturing). Moreover, this methodology can be easily extended in
order to deal with operational costs too (i.e. pressure drops induced by
heat sink), by simply substituting ηA to T r/V as objective function to be
maximized.
It is worth to mention samples, with the same geometrical features of the
ones presented in this Chapter, have been fabricated in aluminum alloy
by direct metal laser sintering (DMLS) too. The latter is an additive
manufacturing (AM), i.e. ”not subtractive”, technique. Preliminary test
revealed each sample by DMLS experienced similar thermal performances
than counterpart by milling. In the next Chapter peculiarities of DMLS
are further investigated. In particular, artificial roughness by DMLS is
optimized to obtain convective heat transfer performances superior than
67
4. Patterns of micro-protrusions for enhanced convective heat transfer
milled counterparts.
68
5. Rough surfaces with enhanced
heat transfer by direct metal
laser sintering
In Chapter 4 diamond protruded patterns (DPPs) produced by both additive manufacturing (AM) and milling have been fabricated and convective
heat transfer coefficient has been measured by mean of experimental rig described in Chapter 3. In particular, AM samples have been manufactured
in aluminum alloy by direct metal laser sintering (DMLS). Thermal characterization reveals DPPs produced by AM have similar performance than
milled ones. Nevertheless, AM allows heat transfer performances higher
than traditional manufacturing techniques, when its peculiarities are properly exploited. Aiming to unveil potentiality of AM in heat transfer, in
this Chapter different rough surfaces obtained by DMLS are fabricated
and thermally characterized. In fact, surface roughness of parts fabricated
by DMLS can be tuned by controlling DMLS process parameters. As a
result, convective heat transfer enhancement up to 73%, compared with
smooth surfaces by milling, is demonstrated. Contents of this Chapter can
be also found in [3].
5.1. Motivations
Additive manufacturing (AM) techniques (often referred to as layer manufacturing or rapid prototyping) allow to build highly complex components
from a three-dimensional computer-aided design (CAD) model without
part-specific tooling [90]. Selective Laser Melting (SLM) (also referred to
as direct metal laser sintering - DMLS) is an AM process where a laser
source selectively scans a powder bed according to the CAD-data of the
part to be produced. The high intensity laser beam makes it possible to
completely melt and fuse the metal powder particles together to obtain
almost fully dense parts. Successive layers of metal powder particles are
69
5. Rough surfaces with enhanced heat transfer by direct metal laser sintering
melted and consolidated on top of each other resulting in near-net-shaped
parts [90]. Research in recent years has identified the potential of this process to build metallic components that can act as functional prototypes.
The ability of SLM to produce complex three-dimensional structures with
features that would be difficult if not impossible to manufacture using
conventional methods has been already explored for building heat sinks
[91], as well as miniature heat exchangers and radiators [39]. Moreover,
with the proper choice of input conditions, DMLS can build full dense
parts with mechanical properties equivalent or even superior to those of
parts produced by conventional manufacturing [92, 93]. Finally, the surface morphology of these parts can also be tuned, in order to produce
artificial roughness with some desired features.
The Chapter is organized as follows. Samples manufacturing methodology
is discussed in detail in Section 5.2; Morphological and radiative characterization of rough surfaces is reported in Section 5.3; Experimental data
on convective heat transfer measurements are discussed in Section. 5.4.
Finally, in Section 5.5, conclusions are drawn.
5.2. Rough surfaces by direct metal laser
sintering (DMLS)
Current state-of-the-art DMLS techniques allow to produce bulk object
without significant porosity. Using optimized process parameters is possible to obtain a residual porosity below 0.8% [93]. Due to its versatility
in terms of both materials and shapes, the main advantage of DMLS is
to produce metal complex-shaped components in one step. In the present
study, all samples are made of AlSiMg alloy supplied by EOS GmbH. The
above alloy comes as a powder, whose element shape, dimensions, size distribution (with volume assumption), chemical composition and percentage
in weight were assessed in a previous work [93]. The aluminum alloy specimens were prepared by DMLS with an EOSINT M270 Xtended version.
In this machine, a powerful Yb (Ytterbium) fiber laser system in an Argon
atmosphere is used to melt powders.
DMLS process starts with the creation of a three-dimensional CAD-model
of an object. Then the model is converted to a STL file format. This file
defines optimal building direction of the physical object and it is based on
small triangles, which determine the accuracy and contours of the whole
70
5.2. Rough surfaces by direct metal laser sintering (DMLS)
object. Then, the support structures are generated and subsequently, together with the STL model, are sliced into horizontal layer of 30 µm thickness. These SLI format files are then transferred to the computer of the
DMLS machine, which now has the necessary information to build up
each layer. The essential operation in the DMLS process is the laser beam
scanning over the surface of a thin powder layer previously deposited on
a substrate. The forming process goes along the scanning direction of the
laser beam. Each cross-section (layer) of the part is sequentially filled with
elongated lines (vectors) of molten powder. The quality of a part produced
by this technology depends strongly on the quality of each single vector
and each single layer. Identification of the optimal process parameters of
laser power, scanning speed and hatching distance is a crucial task because
these parameters happen to be the most influential on the parts characteristics: surface quality, porosity, hardness and mechanical properties [9].
Accuracy and part surface quality has become the focus of AM community
with the increased requirement of prototyped functional parts, enhanced
material properties for strength and dimensional tolerance comparable to
conventionally producible parts. Since the whole object is manufactured
starting from tessellation of a 3D CAD model, the contour of a DMLS part
is a stepped approximation of the contour of the nominal CAD model.
As a result of this, all parts manufactured by AM processes exhibit a
staircase effect. The uniform slicing procedure directly affects the extent
of the staircase effect that appears especially along inclined planes and
curved surfaces. As the inclination angle is reduced or the layer thickness
Figure 5.1: (a) Staircase effect on the DMLS model; (b) Building orientation (See Ref. [3]).
is increased, the stair-effect becomes more pronounced. When the slicing thickness is thinner, the staircase is smaller and the surface will be
smoother. The error associated with the staircase effect can be quantified
71
5. Rough surfaces with enhanced heat transfer by direct metal laser sintering
by considering the cusp height in Figure 5.1(a) which is the maximum distance between the nominal part boundary and the boundary of the part
produced by DMLS. In any building orientation, the part is defined with
its base on the xy-plane, the building direction along the z axis and the
angle ϑ defined as the angle between the vector normal to the face (n) and
the slicing direction (k) - see Figure 5.1(b). When the intersection angle ϑ
is equal to or less than the critical value, the region needs adding support.
The need to improve the surface finish of the parts produced by DMLS
has led to a variety of researches on reducing of the staircase effect on inclined and curved surfaces and on the choice of the process parameters. In
this study, starting from the results obtained previously on the optimization of process parameters on surface finish of AlSiMg sample produced
by DMLS [9], values which can modify and increase the surface roughness
were chosen. Samples dimension were 11.1 × 11.1 × 5 mm and they were
orientated with angles from 90° to 0°. The parts with angles from 40° to
30° show a higher surface roughness due to the staircase effect.
Table 5.1: Thermal properties of parts [12]. Heat treatment (last column)
by annealing process for 2 h at 573 K for stress relieve (See Ref.
[3]).
Thermal conductivity
- in horizontal direction
- in vertical direction
Specific heat capacity
- in horizontal direction
- in vertical direction
As built
Heat treated
103 ± 5 W/m/K
119 ± 5 W/m/K
173 ± 10 W/m/K
175 ± 10 W/m/K
920 ± 50 J/kg/K
910 ± 50 J/kg/K
890 ± 50 J/kg/K
900 ± 50 J/kg/K
However, a higher surface roughness should not be detrimental concerning
the residual sub-surface porosity, otherwise the heat transfer performance
may be negatively affected. To avoid such effect, the laser speed on the
surface and sub-surface region must be kept as constant as possible. This
is not trivial because during scanning a certain time is needed to accelerate
the mirrors to the desired speed. This is due to inertia of mirrors used for
scanning. During this time, the laser beam moves at a non constant speed:
hence more energy is applied at the edges of the part than in the bulk.
To avoid this situation, the mirror is accelerated already before the start
of the part so that it has reached the desired speed before the beginning
of exposure (skywriting option in EOS GmbH technology). This strategy
72
5.2. Rough surfaces by direct metal laser sintering (DMLS)
proved to be effective for building the present samples with extremely low
porosity (see Fig. 5.5). Low porosity ensures very good thermal properties
of parts, which can be improved even further by heat treatment, as shown
in Table 5.1.
(a)
(b)
(c)
(d)
Figure 5.2: Tested samples made of AlSiMg alloy by direct metal laser
sintering (DMLS): (a) sample #1, average roughness Ra = 16
µm; (b) sample #2, Ra = 24 µm; (c) sample #3, Ra = 43 µm;
(d) sample #4, finned surface, roughly Ra = 22 µm as average
on both sides (See Ref. [3]).
After being manufactured and removed from the building platform, five
parallelepiped facets are milled in order to fit into the convective heat sensor presented in Chapter 3. The remaining sample facet maintains the
original roughness due to the DMLS manufacturing and it will be named
rough surface in the following description. The first three samples are
characterized by flat rough surfaces, see subplots (a, b, c) in Fig. 5.2. In
the fourth sample, see subplot (d) in Fig. 5.2, the rough surface has an
additional orthogonal fin of size 11.1 × 10 × 2 mm, in order to explore
finned surfaces as well. Finally, the fifth sample, see Fig. 5.3, is obtained
by milling both horizontal surfaces and fin half sides of the fourth sample.
For convenience, the tested samples (reported in Fig. 5.2) are identified
by the standard average roughness Ra . However, a more sophisticated
surface characterization (with respect to Ra ) will be discussed in the following section. Those samples were obtained by varying the angle between
the rough surface and the hatching DMLS plane in order to explore the
impact of this parameter on the surface morphology and consequently on
the thermal performances.
Figure 5.4 shows the angle of construction of the samples, the process
parameters used for rough surface and the average roughness obtained.
73
5. Rough surfaces with enhanced heat transfer by direct metal laser sintering
Figure 5.3: Example of 3D optical scan of sample #5 made by milling
both horizontal surfaces and fin half sides, after testing sample
#4. The other physical dimensions remain the same (See Ref.
[3]).
Figure 5.4: Process parameters and orientation in the building platform
of the samples produced by DMLS, where P and v are laser
power and scan speed, respectively [9] (See Ref. [3]).
74
5.3. Morphological and radiative characterization of rough surfaces
(a)
(b)
(c)
Figure 5.5: Characterization of the residual porosity of the DMLS samples
by Field Emission Scanning Electron Microscopy (FESEM):
No sub-surface porosity is visible. (a) sample #1; (b) sample
#4, fin root; (c) sample #4, finned surface, fin middle (See
Ref. [3]).
The angle considered was the one comprised between the rough surface
and building platform (rsangle ). The considered samples have extremely
low porosity (see Fig. 5.5). Heat treatment has been applied to all tested
samples, in order to improve further their thermal properties (see Table
5.1 for details). Smooth samples (both in aluminum and copper) made
by milling with Ra ≈ 1 µm were also used as a reference. The latter
roughness value is typical of heat dissipators for electronics, which are
usually obtained by traditional manufacturing techniques, and hence it is
particularly suitable for estimating the relative thermal enhancement.
5.3. Morphological and radiative
characterization of rough surfaces
In this section, a detailed morphological analysis is reported for the tested
samples shown in Fig. 5.2. First of all, the samples were characterized by
a 3D optical scanner ATOS Compact Scan 2M (GOM GmbH) with the
results reported in the subplots (a, c, e) of Fig. 5.6. The latter figures
reveal a complex multi-scale morphology (at least for samples #1 and #3),
which could be ascribed to the contour parameters used together with the
powder adopted. In fact the mean particle diameter ranges from 0.5 to 40
µm, but the small particles are far more (in number) than the bigger ones,
thus creating clusters with complex morphology at the micro-metric scale.
On the other hand, in sample #2, as described in the previous paragraph,
75
5. Rough surfaces with enhanced heat transfer by direct metal laser sintering
(a)
(b)
(c)
(d)
(e)
(f)
Figure 5.6: Surface morphological characterization of flat samples: (a, c,
e) by 3D optical scanner referring to the fluid-dynamic plane
and (b, d, f) by Field Emission Scanning Electron Microscope;
(a, b) sample #1, Ra = 16 µm; (c, d) sample #2, Ra = 24
µm; (e, f) sample #3, Ra = 43 µm (See Ref. [3]).
the rough surface was parallel to the hatching plane, so associated to different building parameters, and this allows the free metal surface (due to
laser melting) to smooth out more homogeneously. It could be noticed
that the FESEM images are reported by planar view, thus it is not simple
to estimate therein the actual height of the peaks.
76
5.3. Morphological and radiative characterization of rough surfaces
In order to make more quantitative analysis, let us introduce the so-called
R-parameters [94] and the S-parameters [95]. First, the arithmetic average
height parameter Ra is defined as
n
Ra =
1X
|zi − zm |,
n i=1
(5.1)
where zi is the height of the generic rough surface point i-th with respect
to the reference plane, zm = zm (s) is the least squares mean line of the
rough profile (not necessarily constant), s is the generalized coordinate of
the profile and n is the number of profile points measured by a rugosimeter.
Clearly, the above definition holds under the assumption of homogeneously
distributed profile points, as usually occurs in this kind of measurements.
Another popular R-parameter is given by Rz , which is the difference in
height between the average of the five highest peaks and the five lowest
valleys along the assessment length of the profile. This value is usually
larger than Rp , which is the maximum height of the linear profile.
Previous parameters have the limitation of referring to a specific profile
measured by the rugosimeter and they may lead to inaccurate estimates for
the whole surface. Hence the S-parameters [95] have been proposed. The
arithmetical mean height of the surface Sa has a definition very similar to
Eq. (5.1), but now zm is the least squares mean plane of the rough profile,
namely zm = zm (s1 , s2 ), where s1 and s2 are the two planar generalized
coordinates. Similarly, Sp is the maximum height of the peak and Sq is the
root mean square height of the surface. Moreover, high order moments are
also commonly used. For example, the skewness Ssk (third order moment)
and the kurtosis Sku (fourth order moment). The sign of Ssk indicates the
predominance of peaks (i.e. Ssk > 0) or valley structures (Ssk < 0) on the
surface as compared to a Gaussian distribution (Ssk = 0). On the other
hand, Sku indicates the presence of inordinately high peaks/deep valleys
(Sku > 3) or lack thereof (Sku < 3) making up the texture with respect
to a Gaussian distribution (Sku = 3). More details can be found in Ref.
[95].
Samples in Fig. 5.2 were characterized in terms of the R-parameters using
a RTP80 instrument (SM instruments) for roughness measurements. On
the other hand, the S-parameters were computed by applying the standard
definitions [95] to the three-dimensional profiles obtained by the optical
scanner (where, in order to apply the previous definitions, an interpolated
homogeneous mesh was adopted). All results are reported in Table 5.2.
The tested sample surfaces show a peak distribution close to a Gaussian,
77
5. Rough surfaces with enhanced heat transfer by direct metal laser sintering
Table 5.2: Morphological statistical moments of tested samples (see Fig.
5.2): R-parameters (Rz and average Ra ); S-parameters (maximum Sp , average Sa , root mean square Sq , kurtosis Sku and
skewness Ssk ). For sample #4, left and right denote the corresponding sides of the fin. Ar is the roughness surface area and
A is the reference planar area (See Ref. [3]).
Sample
#1
#2
#3
#4 (left)
#4 (right)
Rz
[µm]
79.1
132.6
237.8
99.5
108.8
Ra
[µm]
15.8
23.5
43.0
20.6
23.9
Sp
[µm]
41
89
118
38
67
Sa
[µm]
12
27
36
15
25
Sq
[µm]
15
34
45
18
31
Sku
Ssk
3.01
2.88
2.78
2.89
2.59
0.31
0.32
0.32
-0.21
0.12
Ar /A
[%]
1.1
3.4
6.9
-
i.e. Sku ≈ 3 and Ssk ≈ 0. More importantly, the flat surfaces reveal
Sa /Sp ≈ 0.3, while both sides of the fin have Sa /Sp ≈ 0.4.
Table 5.3: Estimated emissivity of tested samples (see Fig. 5.2): Al refer
to milled smooth samples (Ra ≈ 1 µm) used as reference for
computing heat transfer enhancement (See Ref. [3]).
Sample
(see Fig. 5.2)
Al
#1
#2
#3
Ra
[µm]
1
16
24
43
Real
[℃]
50.5
55.5
52.5
43.9
Estimated
[℃]
50.8
55.6
52.0
43.0
0.10
0.35
0.20
0.39
It is well known that roughness can influence the surface emissivity and
consequently radiative heat transfer. Since the present study focuses on
convective heat transfer only, the contribution due to radiative heat transfer is removed by post-processing the experimental data. To this end,
emissivity of surfaces is estimated through methodology described in 3.4.2.
The results are reported in Table 5.3. As expected, these data clearly show
that the rough samples present higher emissivity compared to the smooth
one, although no evident relationship between the emissivity and the average roughness Ra was found. The higher emissivities of sample #1 and
#3 might be explained by the multi-scale morphology, already pointed out
78
5.4. Experimental results
by the FESEM analysis (see Fig. 5.6).
5.4. Experimental results
In this section, the experimental data and the measured heat transfer
enhancements are reported for the tested samples. The experimental data
about convective heat transfer (sample #1, #2 and #3 in Fig. 5.2) are
reported in Fig. 5.7 in terms of the Nusselt number N uL and the Reynolds
number ReL defined in Chapter 3.
As pointed out in Chapter 3, Maddox & Mudawar [8] worked with a similar
setup and already realized that the heating edge is the appropriate length
(more than the channel hydraulic diameter) for scaling the experimental
results. The latter evidence was later confirmed in Ref. [72]. For this
reason, the experimental results are presented in terms of NuL and ReL .
140
120
NuL/Pr
0.33
100
80
60
Ra=1 µm
40
Ra=16 µm
Ra=24 µm
20
Ra=43 µm
0.5
1
ReL
1.5
2
4
x 10
Figure 5.7: Experimental data about convective heat transfer (sample #1,
#2 and #3, see Fig. 5.2). Smooth sample (Ra ≈ 1 µm) with
the identical geometry was used as reference (See Ref. [3]).
79
5. Rough surfaces with enhanced heat transfer by direct metal laser sintering
Table 5.4: Experimental data about convective heat transfer for the flat
reference, i.e. Ra ≈ 1 µm (See Ref. [3]).
v
[m/s]
3.4
4.4
5.4
6.4
7.4
8.4
9.4
9.4
10.5
10.5
11.5
12.4
13.4
14.4
15.4
ReL
3.49×103
4.53×103
5.58×103
6.66×103
7.75×103
8.84×103
9.94×103
9.94×103
1.12×104
1.12×104
1.23×104
1.33×104
1.44×104
1.55×104
1.65×104
Ts
[K]
335.0
331.0
327.2
324.2
321.2
319.9
318.2
317.2
316.4
316.5
315.3
314.3
313.3
312.5
312.0
Ta
[K]
302.4
302.2
302.2
302.5
301.9
301.4
300.7
300.4
300.4
300.8
300.4
300.4
300.3
300.4
300.5
Vh2
Rh
[W ]
0.1271
0.1271
0.1270
0.1270
0.1270
0.1270
0.1269
0.1275
0.1274
0.1273
0.1274
0.1273
0.1273
0.1273
0.1274
h
[W/m2 K]
30.80
35.10
40.58
46.75
52.67
54.95
58.08
60.96
64.24
65.00
68.85
74.19
79.07
84.75
88.97
NuL
Pr1/3
26.47
30.17
34.88
40.17
45.27
47.23
49.91
52.39
55.21
55.86
59.17
63.76
67.96
72.83
76.47
σh
[%]
6.55
5.97
5.48
5.14
4.88
4.79
4.69
4.65
4.59
4.58
4.52
4.46
4.42
4.38
4.36
First of all, and more importantly, the rough surfaces made by direct metal
laser sintering (DMLS) show an enhanced convective heat transfer. In
particular, even though the average roughness Ra is not the best parameter
to scale the heat transfer enhancement (see [3]), as expected the rougher
the better. For a more quantitative analysis, the experimental data of the
smoothest Ra ≈ 1 µm reference surface are reported in Table 5.4 and those
of the roughest Ra = 43 µm sample #3 are reported in Table 5.5. Defining
the heat transfer enhancement E as the percentage increase of the rough
surface for convective heat transfer with respect to the smoothest reference
(assumed representative of milling processes), the sample #3 showed a
peak enhancement of 73% and an average of 63%. This enhancement
could not be simply explained in terms of effective area increase, as visible
in Table 5.2.
80
5.4. Experimental results
Table 5.5: Experimental data about convective heat transfer for the sample
#3, i.e. Ra = 43 µm (See Ref. [3]).
v
[m/s]
3.3
4.4
5.4
6.5
7.3
8.4
9.4
10.4
11.4
12.4
13.4
14.4
15.4
ReL
3.39×103
4.53×103
5.58×103
6.77×103
7.64×103
8.84×103
9.94×103
1.10×104
1.22×104
1.33×104
1.44×104
1.55×104
1.65×104
Ts
[K]
324.2
321.7
319.2
316.7
315.0
311.1
310.4
309.7
309.1
308.7
308.1
307.8
307.6
Ta
[K]
303.5
303.5
303.5
303.2
302.8
300.5
300.6
300.4
300.5
300.5
300.4
300.4
300.4
Vh2
Rh
[W ]
0.1293
0.1293
0.1292
0.1290
0.1289
0.1280
0.1276
0.1274
0.1273
0.1268
0.1266
0.1264
0.1262
h
[W/m2 K]
47.82
54.87
63.98
74.90
82.66
95.04
102.74
108.93
116.58
121.85
131.37
135.91
139.91
NuL
Pr1/3
41.10
47.16
54.98
64.37
71.04
81.68
88.30
93.62
100.19
104.72
112.91
116.80
120.24
σh
[%]
5.21
4.96
4.78
4.65
4.57
4.52
4.49
4.48
4.47
4.47
4.47
4.47
4.47
Table 5.6: Experimental data about convective heat transfer for the (single) finned reference (Ra ≈ 1 µm, smooth). For computing
the average convective heat transfer coefficient and the Nusselt
number, the total sample surface area was used (See Ref. [3]).
v
[m/s]
3.4
4.4
5.4
6.4
7.4
8.4
9.4
10.3
11.2
12.5
13.4
14.5
15.4
ReL
3.54×103
4.59×103
5.66×103
6.75×103
7.85×103
8.96×103
1.01×104
1.11×104
1.21×104
1.35×104
1.45×104
1.58×104
1.68×104
Ts
[K]
315.2
312.4
310.1
308.3
307.0
306.1
305.7
305.4
305.0
304.5
304.3
303.8
303.6
Ta
[K]
297.9
297.8
297.5
297.4
297.3
297.4
297.6
297.7
297.7
297.8
297.7
297.8
297.7
Vh2
Rh
[W ]
0.3605
0.3601
0.3592
0.3591
0.3587
0.3582
0.3580
0.3576
0.3575
0.3570
0.3662
0.3656
0.3653
h
[W/m2 K]
52.85
63.05
73.92
84.92
96.22
106.49
114.77
120.77
129.20
139.55
147.07
159.28
164.01
NuL
Pr1/3
45.69
54.52
63.91
73.42
83.20
92.07
99.23
104.41
111.70
120.65
127.16
137.72
141.80
σh
[%]
3.38
3.02
2.78
2.64
2.56
2.53
2.51
2.50
2.50
2.50
2.49
2.51
2.52
81
5. Rough surfaces with enhanced heat transfer by direct metal laser sintering
200
NuL/Pr0.33
150
100
Ra=1 µm
Rua=22 µm
50
Rda=22 µm
R =22 µm
a
0.5
1
Re
1.5
2
4
x 10
L
Figure 5.8: Experimental data about convective heat transfer of finned
surfaces (sample #4 and #5, see Figs. 5.2 and 5.3). Smooth
sample (Ra ≈ 1 µm) with the identical geometry was used as
reference. Rau and Rad refer to sample #5 mounted with smooth
half fin upstream and downstream, respectively (See Ref. [3]).
Table 5.7: Experimental data about convective heat transfer for the sample #4 (Ra = 22 µm, maximum roughness). For computing
the average convective heat transfer coefficient and the Nusselt
number, the total sample surface area was used (See Ref. [3]).
v
[m/s]
3.4
4.4
5.3
6.4
7.3
8.4
9.3
10.4
11.4
12.4
13.4
14.4
15.5
82
ReL
3.54×103
4.59×103
5.55×103
6.75×103
7.74×103
8.96×103
9.96×103
1.12×104
1.23×104
1.34×104
1.45×104
1.57×104
1.69×104
Ts
[K]
323.3
319.3
318.5
315.2
313.9
313.8
312.1
311.6
311.1
311.4
310.0
309.6
310.0
Ta
[K]
304.7
303.3
304.6
303.2
303.0
304.0
303.0
303.0
303.1
304.0
303.0
303.1
303.8
Vh2
Rh
[W ]
0.5229
0.5251
0.5195
0.5240
0.5233
0.5230
0.5247
0.5243
0.5238
0.5184
0.5235
0.5235
0.5235
h
[W/m2 K]
72.26
84.73
97.58
114.47
127.22
141.75
153.52
163.67
176.88
187.99
203.07
216.42
229.52
NuL
Pr1/3
62.48
73.26
84.37
98.97
109.99
122.55
132.73
141.51
152.93
162.54
175.58
187.12
198.44
σh
[%]
2.89
2.68
2.58
2.46
2.42
2.40
2.38
2.38
2.38
2.40
2.41
2.42
2.45
5.4. Experimental results
In order to prove that the previous enhancements are not limited to flat
surfaces only, some experimental tests were performed with (single) finned
rough surfaces as well. The experimental data about convective heat transfer of finned surfaces (sample #4 and #5, see Figs. 5.2 and 5.3) are reported in Fig. 5.8, again in terms of the Nusselt number NuL = h L/λ and
ReL , where h is the average convective heat transfer coefficient for finned
surfaces. For a more quantitative analysis, the experimental data of the
smoothest Ra ≈ 1 µm finned reference surface are reported in Table 5.6
and those of the roughest Ra = 22 µm sample #4 are reported in Table
5.7. The heat transfer enhancement is confirmed in this case as well: The
sample #4 showed a peak enhancement of 40 % and an average of 35 %.
The enhancement is smaller than that the one observed in the case of flat
surfaces (roughly half). First, It should be noticed that the roughness
parameters for the finned sample #4 are smaller than those of the roughest flat sample #3, as reported in Table 5.2. Second, the fluid-dynamic
conditions of the finned sample are completely different than those considered in the previous case: especially the fin tip yields the development of
a new velocity boundary layer, superposing with the developing thermal
boundary layer.
Further tests were designed to investigate the distribution of convective
heat transfer on the latter sample. The fin area is 3/4 the total convective
area. By assuming also that convective heat transfer coefficient on the
horizontal surfaces of the smooth finned sample is equal to that on the
smooth flat sample, it is possible to find out that convective heat transfer
coefficient on fin sides is almost twice than that on horizontal surfaces.
Hence it is important to investigate particularly the fin sides. The sample
#5 (see Fig. 5.3) was made by milling horizontal surfaces and half of the
fin sides of the previous sample #4. Consequently it was tested once by
mounting it with smooth half fin upstream and once downstream (corresponding to Rau and Rad in Fig. 5.8). We found that smoothing (upstream)
half of the fin sides the convective heat transfer is almost cut by half as
well, confirming that most of the heat transfer is due to the fin. However,
mounting the same sample #5 in downstream setup, the heat transfer reduction is even larger: This indicates that rough regions of the fin sides are
more effective when farther from the leading edge of the boundary layer.
Finally, it is worth to discuss influence of roughness on friction factor,
i.e. pressure drops. As discussed in Chapter 2, heat transfer devices
performance criteria usually evaluates both thermal (heat transfer) and
fluid-dynamics (pressure drops) performances, in order to guarantee the
desired heat transfer rate with minimum operating cost (pumping power).
83
5. Rough surfaces with enhanced heat transfer by direct metal laser sintering
In this preliminary study, the sole heat transfer performances are measured. Nevertheless, it is possible to estimate friction factor of different
flat rough surfaces through the Reynolds analogy (see [38] and Colburn’s
relation therein). That links the friction factor with the convective heat
transfer, namely N u ∝ f . Under this assumption, it could be easily verified that aerothermal efficiency ηA ∝ (N u/N uref )2/3 , suggesting that
rough surfaces experiencing enhanced heat transfer could guarantee enhanced aerothermal efficiency, too. The Reynolds analogy was derived
under strong simplifying assumptions, which may not be applicable to any
rough surface with any possible morphology. However this represents a
first step, which requires further experimental verification.
5.5. Discussion
In this Chapter, the potential of the DMLS artificial roughness are experimentally investigate and optimized for convective heat transfer enhancement, in manufacturing flat and finned heat sinks. For rough flat
surfaces, a peak of convective heat transfer enhancement of 73% (63% on
average) is experienced, while, for rough (single) finned surfaces, a peak
enhancement of 40% (35% on average) is found. Owing to a huge space of
process parameters to be explored, the present work can be regarded as a
first (but essential) step aiming at unveiling the great potential of DMLS
in high efficiency heat transfer devices. Moreover, the presented results
can be easily extended to other industrial sectors involving turbulent flows
over walls. Please refer to [3] for additional information (e.g. theoretical
model). Beyond the possibility to control surface roughness, a popular
peculiarity of DMLS is the extreme flexibility in shapes of the fabricated
parts. This feature is investigated in the following chapter to design high
efficiency heat transfer devices.
84
6. Pitot tube based heat
exchanger by DMLS
Peculiar features of DMLS are possibility to control surface roughness and
capability of fabricating complex 3D structured. The first one has been
investigated in Chapter 5; The following chapter focuses on the second.
Here, a novel heat transfer device is conceived, designed and tested. Its
unusual morphology is purposely designed to exploit ”Pitot tube” effect
to generate secondary air flows aiming to enhance heat transfer. That
device is extremely challenging (if not impossible) to be fabricated by traditional manufacturing techniques. Here it is easily fabricated in one step
by DMLS, taking advance of the extreme flexibility in shape of manufactured parts. Higher heat transfer efficiency (i.e. convective heat flux)
is reached, when compared with a standard reference device. More important, here the aim is to shed light additive manufacturing can lead a
revolution in designing next generation heat transfer devices, when its versatility in shapes is fully exploited. Contents of this Chapter can be also
found in [10].
6.1. Motivations
In this work, a novel heat transfer device based on Pitot tube effect is
designed and manufactured by AM. Starting from a conventional plate fin
heat sink (PFHS) considered as reference setup, that has been re-designed
by introducing (i) hollow fins and, on the top of fin array, (ii) a pressure
plug, which is in communication with (iii) several openings at the bottom of
hollow fins. The basic idea is exploiting the Pitot tube effect for inducing
secondary flows orthogonal to the main flow within fins. Consequently,
heat transfer augmentation is achieved in the region where the velocity
field is less vigorous (i.e. bottom of fins), by perturbing fluid-dynamics
structures (i.e. boundary layers).
85
6. Pitot tube based heat exchanger by DMLS
The Chapter is organized as follows: In Section 6.2, the heat exchanger
design is described; In Section 6.3, the experimental characterization of the
Pitot and reference heat exchanger is presented and examined; In Section
6.4, conclusions are drawn and perspectives are discussed.
6.2. Description of Pitot heat exchanger
Two heat exchangers have been manufactured, tested and compared in
this Chapter, namely the proposed innovative heat exchanger and the corresponding reference one. The heat exchanger with Pitot tubes has been
manufactured by DMLS, according to the process discussed in Section 5.2.
Concerning process parameters, those have been already reported in Tab.
5.1 (refer to sample #1); Nevertheless, a more detailed description of them
can be found in [9] (Tab. 1).
As depicted in Fig. 6.1, the Pitot heat exchanger is made of: (i) a 11x11x5
mm3 parallelepiped; (ii) three 2x10x10 mm3 hollow fins; (iii) a 11x10x6
mm3 pressure plug (i.e. stagnation pressure tap). The parallelepiped is
the bottom part of heat exchanger, whereas hollow fins are located on its
upper side. Each fin is equally spaced from neighboring ones by 2 mm,
and fin walls are 0.5 mm thick. Hence, the cavity volume is 1x9x10 mm3
in each fin. Moreover, eight ellipsoidal openings (i.e. static pressure taps)
have been placed at the bottom of each fin wall. The latter openings
have dimensions 1.6x0.8 mm2 , and are arranged along three rows in a
staggered configuration. Finally, the walls of the pressure plug are 1 mm
tick laterally, while the remaining ones are 0.5 mm tick. The present heat
exchanger has been manufactured in one step by DMLS, whereas bottom
and lateral sides of the parallelepiped have been refined by milling, in order
to properly insert it into the housing of the heat flux sensor described in
Chapter 3.
A reference heat exchanger (i.e. PFHS) made of copper and manufactured
by traditional milling has been also realized and tested for comparison
purposes (Fig. 6.2). This conventional heat exchanger consists of a parallelepiped with three fins, with the same dimensions as in the Pitot heat
exchanger; however, it differs from the Pitot heat exchanger as it does not
have hollow fins, pressure plug and openings.
86
6.2. Description of Pitot heat exchanger
(a)
(b)
(c)
(d)
(e)
(f)
Figure 6.1: Heat exchanger with Pitot tubes embedded into the fins. (a)
Picture of the prototype. Drawings of the prototype: (b) isometric view; (c, f) front views; (d, e) lateral views. Dashed
lines in (c, e) define the cross-sections represented in (d, f),
(See Ref. [10]).
87
6. Pitot tube based heat exchanger by DMLS
Figure 6.2: Reference heat exchanger: plate fin heat sink - PFHS (See Ref.
[10]).
6.3. Experimental characterization
The Pitot heat exchanger has been first tested in the open configuration
(Fig. 6.1). For the sake of comparison, a closed configuration has been
also tested, where a thin copper foil is glued at the bottom of the pressure
plug, thus preventing the Pitot effect without affecting the overall shape
of the heat exchanger. In fact, in the closed configuration, the foil is intended to stop the secondary flows at the bottom of fins, by inhibiting the
fluid communication between pressure plug and fin openings. Testing the
Pitot heat exchanger in both open and closed configuration is crucial to
demonstrate the impact of the sole Pitot effect on heat transfer enhancement. In fact, the heat transfer enhancement due to secondary flows can
be quantified by a direct comparison between the two configurations.
Experimental characterization has been carried on by the experimental rig
described in Chapter 3. Convective thermal transmittance (T r = hA) of
heat exchangers is reported in Fig. 6.3 as function of the heated edge,
average velocity based Reynolds number ReL = vL/ν, defined in Chapter
3.
It is worthwhile to note that the thermal transmittance of the Pitot heat
exchanger with open configuration is higher than the closed one, which
is in turn higher than the transmittance of the reference heat exchanger
(i.e. PFHS). The superior performance of the open Pitot configuration as
compared to the closed one demonstrates the heat transfer improvement
by the secondary flows due to Pitot effect.
88
6.3. Experimental characterization
0.3
Tr [W/K]
0.25
Open
Closed
Ref
0.2
0.15
0.1
0.05
2000
Figure 6.3:
4000
6000
8000 10000 12000 14000 16000
ReL
Convective thermal transmittance measured at different
Reynolds numbers, for open Pitot (purple squares), closed
Pitot (blue stars), and reference (pink crosses) heat exchangers
(See Ref. [10]).
89
6. Pitot tube based heat exchanger by DMLS
As expected, the pressure increase in the plug induces a secondary air
flow circulation along the fin cavities, which exits from the openings at
the bottom of fin array (Fig. 6.4a). Hence, the resulting convective heat
transfer enhancement stems from two phenomena. First, the secondary
air flow along the fin cavities cools down the inner fin walls, therefore
an additional heat transfer area is involved in the heat transfer process.
Second, air flows out of the openings orthogonally to the primary air flow
and fin walls, thus interfering with the boundary layer and consequently
enhancing the local heat transfer coefficient on the external fin walls.
(a)
(b)
Figure 6.4: Schematics of the air flow patterns in the Pitot heat exchanger
with (a) open and (b) closed configurations (See Ref. [10]).
The Pitot heat exchanger with closed configuration shows thermal transmittances lower than the open one, because the fluid separation between
pressure plug and fins cavities prevents the creation of secondary air flows.
Hence, the kinetic energy of air entering the tap is dissipated by eddies
(Fig. 6.4b). From preliminary results, the open Pitot configuration exhibits maximum and average T r enhancements up to 38% and 32%, respectively, as compared to the closed ones.
Finally, It is worth to stress that the reference heat exchanger (i.e PFHS)
90
6.4. Discussion
has the lowest thermal transmittance among the tested configurations.
This happens because the conventional heat exchanger benefits neither
of the additional heat transfer area provided by the pressure plug (still
present in the closed Pitot configuration), nor of the secondary flows induced by the Pitot tubes. Additionally, the innovative heat exchanger can
also benefit of the artificial roughness readily available in parts manufactured by AM, as extensively reported in Chapter 5. In conclusion, the
proposed heat exchanger based on the Pitot tube effect shows a maximum
(average) enhancement in convective thermal transmittance of 95% (88%),
as compared to the reference case. It is worth to emphasize that the proposed solution is a passive heat transfer augmentation technique, which
does not need any additional energy source to work.
Concerning augmentation in pressure drops, it should be highlighted that,
generally, behavior in terms of pressure drops of reference PFHS and Pitot
heat exchanger are expected to be different. In fact, introduction of pressure plug implies augmentation of frontal cross section of heat exchanger.
Moreover, secondary air flows from static tap placed on the fins, perturbing fluid-dynamic behaviour, can also affect overall pressure drops.
As discussed in Sections 2.2 and 2.4, type of configuration (shrouded or
unshrouded) plays a crucial role in determining the relevance of pressure drops induced by different heat exchangers (PFHS or Pitot). In the
proposed work, both Pitot heat exchanger and PFHS are studied in unshrouded configurations. Moreover, frontal cross section of both the heat
sinks is very small (about 2 cm2 ) if compared with overall wind tunnel
cross section, i.e. nearly 360 cm2 . Hence, as discussed in Section 2.2,
eventual augmentation in pressure drop induced by Pitot heat exchanger
do not lead to augmentation in overall circuit pressure drop. Moreover,
excellent heat transfer performances of Pitot heat exchanger suggest that
increase in pressure drops of Pitot heat exchanger are expected to be nearly
negligible, since they do not lead to augmentation of bypass effect. Hence,
Pitot heat exchanger is supposed to be a valid solution also from the point
of view of pressure drops (i.e. operative costs), in the proposed unshrouded
configuration.
6.4. Discussion
In this study, an unconventional heat exchanger is proposed, which implements an innovative passive technique for heat transfer augmentation.
The proposed device has been designed and manufactured in a single step
91
6. Pitot tube based heat exchanger by DMLS
by exploiting the capabilities and flexibility of direct metal laser sintering
(i.e. selective laser melting) in fabricating complex shaped components.
Given a main flow field, the proposed Pitot heat exchanger induces secondary flows passing through the fin cavities and exiting orthogonally to
the main flow. As a result, this solution significantly improves the convective heat transfer by concurrently (i) increasing heat transfer area and (ii)
enhancing local heat transfer coefficient on fin walls, especially in regions
where the flow field is less vigorous (fin bottom). The latter is achieved
by inducing perturbation in fluid-dynamics structures (i.e. boundary layer
breakage). The reported experiments show up to 95% increase in thermal
performances of Pitot heat exchanger as compared to standard one. The
sole Pitot tube effect is estimated to be responsible of 40% enhancement
in thermal performances.
The preliminary results reported in here are intended to shed light on
the new frontiers that additive manufacturing are opening in heat transfer
engineering. In particular, the extreme geometrical flexibility offered by
additive manufacturing may lead to new ways in conceiving and designing
next-generation heat transfer devices.
92
7. Conclusions and perspectives
7.1. Survey and conclusions
In the present thesis, novel methods devoted to develop high heat transfer efficiency devices have been presented. These methods rely on both
novel manufacturing techniques, belonging to the class of additive manufacturing (AM), and thermal and fluid-dynamics studies and optimization
procedures.
As a first result, optimization of a traditional heat exchanger from a real
application, i.e. million of units produced per year, is presented; That
is manufactured by extrusion. A thermal fluid-dynamic model is experimentally validated (from an industrial experimental test rig) and used for
optimization purposes. Results demonstrate there is room for efficiency
optimization even in well established heat transfer devices configurations
based on traditional manufacturing techniques [1].
Then, an experimental rig for ”in house” thermal characterization is designed. It guarantees high precision measurement of small convective heat
fluxes (forced air) on enhanced solutions investigated hereinafter, namely
micro-structured surfaces and small heat transfer devices. To deal with
that challenge, an innovative convective heat flux sensor is developed. That
exploits the concept of thermal guard to avoid any spurious perturbation
between the flow field and investigated surfaces, while it allows to cancel out terms due to spreading conduction phenomenon. Results demonstrate remarkable accuracy in direct measurement of convective heat fluxes
through this novel concept [4].
Relying on the proposed experimental rig, various methods for enhanced
convective heat transfer are experimentally investigated. Firstly, regular
patterns of micro-protrusions are studied. Effect of fluid-dynamics and geometrical length on heat transfer performances are discussed. More important, they have been applied to develop an optimization procedure tailored
to deal with AM techniques. Results from both experimental investigation
93
7. Conclusions and perspectives
and optimization procedure suggest the existence of an optimal value of
protrusion height, that maximize performance-to-cost ratio for patterns
made by AM [7].
Then, surface roughness of components built by DMLS has been investigated as an augmentation heat transfer technique. Surface roughness
is controlled varying DMLS process parameters and its effect on convective heat transfer is measured. The results demonstrate a remarkable enhancement in convective heat transfer due to DMLS artificial roughness,
in the investigated configurations [3]. That preliminary study unveils the
potential of AM artificial roughness as an heat transfer enhancement techniques. It has been considered, by academic and industrial institutions,
as an important step towards development of next generation gas turbine
components [96–98] and electronic cooling devices [99].
Finally, extreme flexibility in shape of parts built by DMLS is exploited
to design and fabricate in one step an unconventional heat transfer device,
called Pitot heat exchanger. Enhanced heat transfer efficiency is achieved,
with regard to standard heat exchangers. Nevertheless, the most important achievement has been to highlight unusual morphologies allowed by
AM can pave the way to revolutionary changes in conceiving and designing
heat transfer components [10].
7.2. Outlook and perspectives
Additive manufacturing, also called 3D printing, is a manufacturing technique born nearly 30 years ago. In last decades AM evolved, in order
to process different materials, increase quality of fabricated parts and reduce costs. As a result, nowadays it allows to fabricate complex 3D parts
in metallic alloys with low bulk porosity, hence guaranteeing high thermal conductivity and remarkable mechanical properties. Moreover, it has
been demonstrated to be a cost effective choice with regard to traditional
manufacturing technique, in producing small batch (hundreds per years)
of parts. AM is currently used by aerospace companies to produce components such as gas turbine blades. High efficiency heat transfer is crucial
in these components [100].
That encouraging growth could open the possibility AM will be used for
mass production of large amount of items, in the future. Probably, AM
will integrates traditional manufacturing techniques [101]. Even, has been
argued AM could pave the way to a third industrial revolution [102].
94
7.2. Outlook and perspectives
Key of present and future development of AM lays in the so called ”think
additive” attitude. It means focus on peculiar features of AM, not allowed
by traditional techniques, and exploit them. They are flexibility in shapes
of built parts, capability of built in one piece complex systems fabricated
so far connecting together many different parts, possibility to reduce material used to fabricate them (hence reducing weight and costs), possibility
to tune surface roughness. ”Think additive” advice has been already receipt in field of structural mechanics where peculiarities of AM are used to
develop more efficient, reliable and lighter devices. See as example structural supports depicted in [103] and fuel nozzles for gas turbines described
in [104, 105].
On the other hand, ”think additive” attitude has not been receipt yet in
the field of thermal system design. Very few examples of such a spirit in
developing heat transfer devices can be found, so far (e.g. [99]). Nevertheless, Additive manufacturing is used nowadays in application where
thermal management is a crucial issue. This work is expected to encourage
scientific and industrial community toward a shift in approaching design
of new technological solutions for heat transfer based on AM.
95
8. Conflicts of Interest
The author declares no conflict of interest. Permissions to reproduce contents from [3, 4, 7, 10] have been granted by the publisher through Copyright Clearance Center service.
97
9. Curriculum Vitae
Luigi Ventola
Personal Data
Date of birth:
Sex:
Place of birth:
Citizen of:
9th April 1987
male
Avellino (Italy)
Italy
Education
• PhD thesis (2013-2016)
– Title: High-efficiency heat transfer devices by innovative manufacturing techniques
– Tutors: Prof. Dr. P. Asinari and Dr. E. Chiavazzo
– Department: Energy department
– Place: Polytechnic of Turin (Italy)
• Master degree in Energy and Nuclear Engineering (20082011)
– Title: Computational fluid dynamics and population balance
based modeling of fluidized systems for gasification.
– Tutor: Prof. Dr. D.L. Marchisio
– Department: Chemical engineering
99
9. Curriculum Vitae
– Place: Polytechnic of Turin (Italy)
Work experience
• Research fellow (2011-2012)
– Place: Polytechnic of Turin (Italy)
• Ventilation system analyst (2011)
– Place: Cantene S.r.l., Turin (Italy)
• Production engineer (2011)
– Place: Ahlstrom Turin S.p.A., Mathi, Turin (Italy)
Publications
• L. Ventola, G. Curcuruto, M. Fasano, S. Fotia, V. Pugliese, D.,
E. Chiavazzo, and P. Asinari. Unshrouded plate fin heat sinks for
electronics cooling: Validation of a comprehensive thermal model
and cost optimization in semi-active configuration. under review for
publication on MDPI energies, 2016.
• M. Fasano, L. Ventola, F. Calignano, D. Manfredi, E. P. Ambrosio,
E. Chiavazzo, and P. Asinari. Passive heat transfer enhancement by
3D printed Pitot tube based heat sink. International Communications in Heat and Mass Transfer, 74:36 – 39, 2016.
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Appendix
115
A. Computational fluid dynamics
(CFD) model
A computational fluid dynamics (CFD) model was used to obtain the
mathematical relation between average and axial velocities in the wind
1.0162
channel described in Chapter 3, i.e. ReD = 0.694 (RexD )
(see Section
3.4.2). A rectangular flow channel with the same section as the real one,
but much longer entrance length (roughly 60 hydraulic diameters) was
considered. The reason being that the constant velocity profile used as inlet
condition requires a longer length than real one to develop asymptotically.
As a matter of fact, the throttling valve in the real channel is an effective
turbulence promoter, which makes the developing length much shorter.
The numerical model required roughly 2 millions of computational cells
in order to obtain mesh-independent results and a special care was used
in meshing the boundary layer. In particular, the maximum y + = ∆y/y0
(normalized dimensionless distance of the first cell centroid from the wall)
used in the simulations at the maximum Reynolds number was 1.9, i.e.
the viscous sublayer (< 5y0 ) was correctly meshed [106]. The standard
k − turbulence model was adopted for closing the Reynolds-averaged
Navier-Stokes (RANS) equations [106]. Because the near-wall mesh was
fine enough to resolve the viscous sublayer, the adopted enhanced wall
treatment reduces to the traditional two-layer zonal model [106].
A second model has been developed to compute heat transfer coefficient
through the sample. The main goal of this second model was to compute
the convective heat transfer coefficient h, under different flow conditions.
The numerical simulations were used to support the experimental results
obtained by the proposed sensor, at least in case of flat surfaces. Fully
developed turbulent velocity profile, obtained from the previous model,
was imposed at the inlet of the computational domain. The sample and
the guard were modeled as an isothermal surface with a temperature higher
than that of air, such that the temperature difference Ts − Ta was roughly
the same as in the experimental measurements. In this second model, a
length of 0.69 m, was considered because the fully developed inlet profiles
117
A. Computational fluid dynamics (CFD) model
were already available. The mesh of the cross section was the same as
the previous model. On the other hand, a fine homogeneous mesh with
1 mm of grid spacing was chosen along the fluid flow, but close to the
upstream edge of the sensor guard, where a finer mesh of 0.1 mm spacing
was necessary. These choices granted mesh-independent results. Overall,
the above numerical model required roughly 6 millions of computational
cells.
For both previous models, some simulations were performed for validation purposes in the following range 3 × 104 ≤ ReD ≤ 17 × 104 (which
is consistent with the experiments reported in this work). Assuming the
smooth channels, the numerical results were compared in terms of the
Darcy friction factor and the Nusselt number against the Blasius correlation and Gnielinski correlation, respectively [38]. The maximum deviations
between the numerical results and the phenomenological correlations were
6.7 % and 2.1 % respectively.
118
B. Data regression procedure
In the following, the details of data regression presented in Section 4.3 are
exposed. Being { ∆TVrR } the (9 × 1) column vector whose i-th component
is the value of ∆TVrR of the i-th sample, we impose:
∆T rR
= [M ]{C},
(B.1)
V
where [M ] is a (9 × 9) matrix and {C} is the (9 × 1) column vector of
model constants defined in Section 4.3. Being {Mi }, the i-th row of [M ],
defined as:
!
!
(
2!
2!
2
d
d
d
d
V
V
A
A
cp
cp ,
,
, λ
,
,
{Mi } =
,
λ
An
AY0
An
AY0
i
i
i
i
i
i
!
!
!
!)
d
d
d
d
A
A
V
V
c
c
λp
, λp
,
.
An
AY0
An
AY0
i
i
i
i
i
i
(B.2)
{Mi } is a vector containing
all the geometrical features of the i-th sample.
Being [M ] and ∆TVrR known, a vector {C} containing the unknown
constants of the model could be obtained as:
∆T rR
{C} = [M ]−1
,
(B.3)
V
where [M ]−1 is the inverse of the [M ] matrix.
119
C. Commercial versus optimized
heat sink
In the following, a representative commercial micro-protrusion patterned
(micro pin-fin) heat sink and the optimized patterns presented in section
4.5 are compared. In particular, the model 662-15 by Wakefield-vette™
extruded heat sink for integrated circuits is chosen as representative commercial heat sink.
Protrusion base edge dc = 1.52 mm, protrusion height Hc = 2.4 mm, root
surface area An,c = (43.5)2 mm2 = 1892 mm2 , and number of protrusions
Nc = 168 of the commercial heat sink are extracted from heat sink data
sheet [107]. Protrusions volume is calculated as Vc = d2c Hc Nc = 931.6
mm3 . Moreover, data sheet [107] reports that 662-15 commercial heat
sink experiences, for air velocity v = 965 LF M = 4.9 m/s, a thermal
resistance of 2.2 K/W , corresponding to a thermal transmittance T rc =
0.45 W/K. The corresponding performance-to-cost ratio is T rc /Vc = 4.88
10−4 W/K/mm3 .
Values of T r for the optimized patterns presented in section 4.5 are referred to the root surface area An = 123 mm2 . Volume of a 662-15
commercial heat sink characterized by root surface area = 123 mm2 is
Vc0 = V An /An,c = 60.6 mm3 , and its transmittance can be estimated as
T rc0 = T rc An /An,c = 0.03 W/K. Moreover, fin efficiency of commercial
heat sinks (made of aluminum) is nearly 100 % (the same that would be
experienced by a copper micro-pin fin heat sink).
Air velocity v = 4.9 m/s corresponds to a Reynolds number ReL = 0.5
10−4 . Hence 662-15 commercial heat sink will be compared to the optimized heat sink that guarantees T ropt = T rc0 = 0.03 W/K at ReL = 0.5
10−4 . Drawings and design parameters of this optimized heat sink can
be found in 1st row of Tab. 4.7, and 3rd row of Tab. 4.4, respectively.
Volume of optimal heat sink is Vopt = 36.8 mm3 , while the corresponding
performance-to-cost ratio is T ropt /Vopt = 8.42 10−4 W/K/mm3 .
121
C. Commercial versus optimized heat sink
In conclusion, optimization procedure based on the proposed model leads
to enhance T r/V , i.e. thermal performance per unit production cost, up
to 73%, with regard to the considered commercial heat sink.
122